ARIELS: Why do you fight for these redundancies? You are like a god to these creatures. Do you really want to live a lonely life in a world that won't accept you?
Before he was Sol Badguy, he was Frederick, a scientist. He was brilliant, but impatient and had difficulty expressing himself with words. Because of this, he preferred to work alone; he got frustrated when others couldn't keep up with him and did not have the patience to explain things clearly. This caused him to alienate most people, but there were at least two that not only tolerated him but grew close to him in spite of his abrasive attitude. These two were his lover, Aria, and their best friend, Asuka.
They were some of the few that he opened up to, willingly sharing his philosophies and passions. Aria admitted to enjoying the down-to-Earth way he spoke, which was a polite way to describe his unfiltered way of talking and his tendency to explain science in vague layman's terms. Even with her, his attitude caused problems: Aria got frustrated that Frederick answered everything using logic, even when she was looking for a sentimental answer.
ARIA: Right? No romance with him. Just nitpicking.
Despite his logical mindset, Frederick was not cold. He joined the Gear Project explicitly due to its potential to cure disease and stop aging. He would also ignore logic if it was convenient: when asked what he would do if he knew the world would end tomorrow and could not be stopped, his answer was to die trying to stop it. He didn't believe anything was impossible, despite all logic saying otherwise. This included finding a cure for Aria's T-infection, despite it being incurable.
Unfortunately, when Asuka transformed Frederick into the first Gear and Aria disappeared, his unhealthy method of dealing with the world was only exacerbated: his loss of Aria made him determined to not get close to anyone ever again out of fear of loss; Asuka's betrayal caused him to develop a cynicism towards all things; being turned into a Gear made his feelings of being an outcast that much more powerful.
FREDERICK: Transforming into something else entirely isn't that much different than death.
Frederick abandoned his name. He was motivated by two things: revenge and guilt. He wanted revenge on Asuka; he waited until the Gear Project was reinstated almost seventy years later and launched guerrilla attacks on associated facilities. The government had no idea who he was and gave him the codename of 'Badguy', which he took as his new name. The only way he knew how to handle what happened to him was by pushing the world away and attacking anyone he could blame.
This only got worse when Justice was born and the Crusades started. Sol blamed himself for what came of Aria, but he also felt guilt for his contribution to the Gear Project. Besides revenge on Asuka--now known as 'That Man'--Sol was determined to destroy every last Gear. Despite hardening himself against the world, Sol could not destroy his compassion: despite his goal being to destroy all Gears, he could not ignore the people around him in danger and saved as many as he could.
He was mostly successful in forcing himself to live a life of seclusion. He made few connections during most of the war, preferring to appear suddenly, destroy Gears, save people, and disappear. The exception was Slayer the vampire who would track down Sol to get to force him to have conversations. Incidentally, Slayer was the one who gave him the name 'Sol' due to "burning" with a passion hotter than the sun and with a potential more blinding. It wasn’t until the end of the war that Sol's life of seclusion was challenged. For multiple reasons, Ky Kiske refused to leave Sol alone; Sol found Ky irritating, but their paths crossed so many times that they had no choice but to get to know each other.
However, Sol was still not interested in getting close to anyone. When he destroyed Justice, he was positive she was Aria transformed into a Gear. He reacted to this by continuing to do what he was doing: keeping the world at bay and hunting That Man for revenge. For him, it was always about revenge; he never wanted to know the truth.
DIZZY: You and I are no longer alone. Please, stand beside me...Help me keep the others from creating new enemies.
The tiny world Sol created continued to be challenged. First, it was only Ky challenging his beliefs, but then it escalated. He learned a company was attempting to create a Justice-style Gear and Sol went there intent on destroying it…only to learn said Gear was a terrified young girl. He wanted to be the heartless monster he thought he was, but he failed to convince himself to destroy her. Instead, he gave her his Gear Cell Suppression Device to help alleviate her discomfort until a proper treatment could be provided.
Immediately, a bigger problem arose: Justice's own daughter, Dizzy, appeared. Again, Sol intended on destroying her because he believed there was no other choice. However, when he met Dizzy, he could not bring himself to hurt her outside of defending himself. This was in no small part due to her kind and innocent nature, but also the fact that, if Justice were Aria, then Justice's daughter would be his daughter. Sol reacted to this revelation the same way he reacted to everything that would require him to deal with his emotions: he ignored it and ran away.
SIN: Yeah, well, sometimes I feel like [Sol]'s so smart he's actually dumb. He gets all grumpy whenever he can't explain something with logic.
Between Ky and Dizzy, Sol had to deal with people actively wanting to be part of his life for the first time in over one hundred years. For the most part, he was able to deal with this by running away from them. However, this became impossible when Ky and Dizzy revealed to Sol that they had a child, Sin. Of course, this meant Sin was his grandson. Due to Ky now being a major world leader and Dizzy still being the daughter of the enemy of humanity, they could not raise a Gear child born out of wedlock without anyone noticing. So, Sol became the guardian and tutor to Sin.
Now with a child to care for, Sol had no choice but to care for another. Due to Sin's massive power as a Gear, Sol needed to act as a role model. He did this with a "do as I say, not as I do" type of teaching: he helped Sin control his power, he made Sin promise never to attack humans, and pounded in other morals that Sol himself was not particularly good at following. Despite constantly criticizing Sin and fighting him (after the kid was grown; that took about three years), Sol prioritized his well-being. After wandering with Sin for three years, Sol's temperament had already taken a major turn to being more subdued. He was still irritable, but no longer in a constant state of rage.
Despite simmering down, Sol was still not ready to open up. At this point, Ky was more than just a young kid trying to show up Sol, but Sol was still terrified of opening up to anyone. Ky pressed Sol about his past: he questioned if Sol actually did want to destroy all Gears; he questioned why Sol cared for Dizzy and Sin; he correctly guessed that Sol was terrified of the truth and of being hurt again. Even Sin managed to contribute: he questioned why Sol wanted to be alone so badly and correctly guessed it was only because Sol wanted to spend all his time feeling sorry for himself. He knew Sol only wanted to be alone to make himself miserable.
ELPHELT: You should know better than anybody else this is pointless!
SOL: Me? What the hell do I know? All I'm trying to hit is one of those memories you seem to have forgotten.
Between dealing with Ky and Sin trying to get him to acknowledge his feelings, Sol had to deal with two new people challenging those feelings: Elphelt and Ramlethal. They were Valentines, making them similar to Gears in that they were created to be enemies of humanity and the two of them were alone in the world. While Sol was trying to convince himself they were unfeeling monsters, Sin befriended them and the rest of their group tried reaching out to them. In a short span of time, he witnessed the sisters suffer, open up to others, and form bonds despite everything. Atop that, they were both partially clones of Aria, giving them--especially Elphelt--a strong physical resemblance to her.
Despite all his efforts, he got attached to them: when Elphelt was possessed by her programming, Sol forced her to regain her own will; when she was kidnapped by her Mother, he was the one to spearhead the operation to save her; when Ramlethal was worrying about her sister's wellbeing and her own newfound emotions, Sol comforted her; when Ramlethal apparently died, he lashed out at That Man for allowing that to happen.
The final things that broke down the walls Sol built around him were the same things that caused him to build it in the first place: Asuka and Aria. Sol learned that being turned into a Gear was not an act of betrayal on the part of Asuka, but rather part of a plan to fulfill Aria's wishes. Aria agreed to be put into cryogenic sleep under the condition that, no matter how long she was asleep, Frederick would be there when she woke up. The only way to do this would be to make Frederick immortal. Asuka turned Frederick into a Gear and Aria into Justice for the sake of saving his best friends' lives and romance. Justice starting the Crusades was an accident.
At that point, Sol was about to have an emotional breakdown. He had to finally acknowledge that, by killing Justice, he killed Aria. He was overwhelmed by emotions he had kept bottled and was vulnerable. But That Man's companion, Jack-O', explained: she resembled Aria even more than Elphelt, but because she was a true clone; she possessed half of Aria's memories; by fusing her with the body of Justice, Aria herself would be revived exactly as she had been the last time Sol saw her.
With these revelations, Sol had no way to hide anymore. Everyone--notably Ky and Sin, amongst others--knew of his past. More importantly, they were able to put the pieces together and they realized Sol was Dizzy's father, making him Sin's grandfather and Ky's father-in-law. Sol tried to prevent everyone from figuring that out so that he wouldn't have to deal with, quote, "weird feelings". In the end, Sol was still cynical and crude, but he had finally faced the things he had spent almost two centuries running away from and finally figured out that being alone was not only impossible, that he didn't want it anymore.
SOL: I make it a habit to be alone. Always have...That's the path I've chosen. The world I've started to like.
SOL: Then all of a sudden a whole bunch of people start to butt into my peaceful life with ideas of their own.
SOL: "I'm in love with this. I want to protect that. I want to rise up. I want to reclaim those. I want to redo everything..."
SOL: You can see how that'll get on a man's nerves...But you know, that's helped me realize something…
SOL: That I'm not just "one". I'm "one of many".