Theory about how Eggman became a villain
No villain becomes one abnormally without some kind of horrid past (unless it were an accident, as with the case of Ovi Kintobor) and I think the Doctor is no exception. There were a couple of times that show how rough his life is. For two examples, AoStH Robotnik’s mother, Momma Robotnik, is meaner, crueler and more ruthless than he is. Also, it was hinted at that Boom Eggman had mommy issues and wanted to impress his oppressive father. Both examples lead me to believe that perhaps the main-game Eggman had an abusive dad growing up and never knew his mom because she passed away. It's an odd conclusion to make, I know, but hear me out.