Eggman and Sage's relationship is so interesting to me because even though they love each other very much, Eggman still doesn't see Sage as a human
Eggman cares for Sage's feelings and safety, gives her presents like toys and shoes, calls her his "dear daughter" and "my girl", laughs at her jokes, always tells her how proud he is of her, is grateful for her protection, griefs her when she dies and doesn't give up until he can restore her.
even though their relationship's development is pretty much stuck on the Egg Memos and not shown in the actual cutscenes, it still manages to be beautifully written. how Eggman sees her as only a tool, starts liking her more than he wants to, thinks she's amazing and adorable, and starts to entertain the idea of seeing her as family - something he hesitates on, because it's not something that would ever cross his mind when he thinks about his machines and also something he never had. notice how the first time he calls her "daughter" is when she's far away, going to meet her death, and she doesn't even hear it. (he never really gets over this hesitation, too.)
however, despite all that, he still doesn't see Sage as a human with autonomy. as we see in IDW, she's offline most of the time when she's not executing a task. sure, he lets her out to play sometimes, he always hears what she has to say, and even... asks for her preferred pronouns? but she doesn't really have much freedom. no matter how much he treasures her, Eggman sees her as a "loyal and effective" program, and made her to be completely subservient to him. this isn't a much healthy relationship.
and you can't even say he sees this kind of relationship as good for his daughter. we can notice that in the Egg Memos where he talks about Tails and Amy.
he thinks that Tails is "wasting his potential lingering in Sonic's shadow", that his "worship" of him is holding him back. well, remind me, who else in this game lives "to serve" someone, giving herself entirely for someone else's goals and principles?
he affirms that it must have been hard for Amy to find herself around someone with such a big ego as Sonic. Eggman is obviously projecting here.
first, his statement is completely incorrect. Sonic might be overly confident, but he doesn't use that to crush others; by any means he held Amy back from running after the best version of herself at any point of their relationship. (except if you consider him looking down on her when she wasn't able to prove she was capable of fighting, saying it's "too dangerous" for her to follow them on their adventures. but it's very reasonable to be worried about someone you always have to save from bad guys and has never really shown to be able to fight for herself. this isn't caused by him having a big ego, and he fully accepts and trusts her after seeing her growth.)
second, you know who has a big ego and does use it to put himself in a pedestral above everybody around him? Eggman, of course.
Eggman believes, even if only in a sub conscious level, that his relationship with Sage might be holding her back from finding her true self and unleashing all of her potential. but why does he seem not to care about that at all? because he sees Sage as someone who exists for him and for him only. the idea of her having as much independence and identity as someone like Tails or Amy sounds quite absurd to him, in a way he doesn't put into words but definitively believes. her being his daughter and perhaps the thing he loves most in the whole world doesn't make her cease to be his A.I., made to serve him and help him conquer the world. as i've heard the fandom say quite a few times, Eggman loves Sage so much because she's an extension of him; he loves her because she's his best creation, and when he praises her and tells her how he's proud of her, he's indirectly praising himself at the same time.
i love their relationship so much because it makes so much sense for Eggman's character. we can make a story where he's able to love someone that isn't him, but his narcissistic nature inhibits him from having a truly selfless, healthy relationship. everything must revolve around him. to change that about his character would kind of defeat its entire purpose, so i'm glad the writers didn't go that route. explore the villain's flaws instead of removing them, that's so much more interesting!
i also wanted to point out this one line:
there's so much pain in his voice when he says this, but notice how he barely hesitates. Sage must fullfil her function; this is why she was created and the reason for her existance. if Sage has to risk her safety and life because of it... well, let it be done.
for example, if we put Sonic and Tails in the same situation, Sonic's response would probably be "if you think that's the right thing to do". Sonic values Tails' freedom more than his safety, in the same way Eggman values Sage's function above her safety. both would be incredibly hurt if they lost them, but stopping them also goes against their principles.
that's it! if you disagree with some of the points i made here PLEASE comment. i created this account with the sole purpose of training my media literacy and interpretation, and being confronted with different opinions is a core part of it. thank you for reading the entire thing, too! ^^