no but really, it does! There´s a reason why the OG Sonic Bible from 1991 had that whole backstory where Eggman was a good guy that Sonic viewed as a fatherly figure, only for him to turn evil due to negative chaos energy and thus forcing Sonic to become a hero to fight him, they were supposed to be tragic from the very start
but since they completely scrapped that backstory from canon, and I'm glad they did, nowadays I just prefer to see it as an interesting way to reframe their dynamic in a really messy, toxic but weirdly sweet way. Eggman knows this kid through his whole life, and it´s obvious that Sonic picked up a few things from the doc (dramatic bows and loud introductions is something I noticed in canon). You never found it weird how many similarities they have despite being polar opposites? Same favorite color, same birthdays, same love for junk food, same stubborness and huge egos? How Sonic had a plane and knew how to fly one, or how he had specialized shoes that could sustain his high velocity friction with the ground before he even met Tails?
maybe they weren't always enemies, maybe when Sonic was just a tad too small he welcomed this strange guy in his life that suddenly appeared on his island because weirdly enough, he made Sonic feel cared for. And while a young Robotnik tried to nurture the trump card that would allow him to seize control over the world, he got a bit more then he bargained for with his irrational attatchment to the chaotic super powered hedgehog he was supposed to use as a tool, a being so pure that loved him unconditionally, no expectations. And what does it matter that the kid betrayed him and the empire the moment he knew he was using his animal friends as fuel for his conquest? It's not like Sonic ever left him alone from then on! Eggman saw as Sonic grew into an admirable adversary, one he respects and even considers as an equal in regards to power and will, and how Eggman played an influential factor in that proccess by being the only constant adult presence in Sonic's life.
and despite Sonic hating the Doc's idea of a perfect world and disagreeing with Eggman at each turn, he'll always be grateful that his arch-nemesis barged into his life and gave him an excuse to leave that island, landing him the opportunity to find himself while exploring the vast world ahead of them
and don't get me wrong they're still cursing at each other and putting themselves in the deadliest of battles to further their own agendas, but in ways where you can see hints of care and yearning for a deeper connection despite them working like crazy to maintain the status quo to keep things lighthearted.
afterall, isn't it tragic that in one hand, the embodiment of freedom would willingly carries the weight of fighting the same megalomaniac over and over in an endless battle in hopes that someday he’ll get some of the affection he truly wants? Never allowing himself to let go of the hope that the ideal of who he thought his father was could be real if Eggman just tried hard enough, especially since Sonic of all people would know that Eggman is capable of loving someone other than himself. While in the other hand we have the embodiment of order and control never allowing himself victory because he couldn't will himself to get rid of the one oddity in his life that gave his brilliance a purpose, that made him strive to become better, sharper and always innovate. He has to defeat Sonic in a grand battle, it's in no way efficient, but he can't imagine his perfect empire's legacy without Sonic in the picture. He's way too important to be treated as a mere obstacle to be rid of and promptly forgotten.
the fact that he created his "perfect version of his son" in the form of Metal Sonic is pretty fucked too, a literal replacement that wants nothing but to kill the original, because despite being the "Better Sonic", the original is always the first in his Master's mind. Must be hard for Sonic too, that Robotnik created a replacement of him that he proudly takes care of and declares as his son... There's actually a pretty good fic on ao3 (Eggfam Troubles by Chilicia_Aselica) that explores Metal and Sonic's dynamic through that lense, I wholy reccommend!
either way i'm sorry for the ramble, I've been obssessed with the idea of Eggman begrudgingly being Sonic's father figure for months now, I've been itching for a moment to infodump for so long and I honestly could keep going on deeper adding my own headcanons if this wasn't already too long and boring
Either way!! Eggdad & Sonic concept dynamic! Keep them in mind, will ya?