I am also not a fan, but since a recent discussion on HN I have been thinking about what I don't like about it.
The conclusion I have come to is more general: I just personally don't like nerd-culture. Having an anime girl (but the same would be the case for an star trek, my litte pony/furry, etc.-themed site) signifies a kind of personality that I don't feel comfortable about, mainly due to the oblivious social awkwardness, but also due to "personal" habits of some people you meet in nerdy spaces. I guess there is something about the fact of not distinguishing between a public presentation and personal interests that this is reminiscent of. For instance: A guy can enjoy model trains, sure, but he is your college at work and always just goes on about model trains (without considering if this interests you or not!), then the fact that this subsumes his personality becomes a bore or even just plain unpleasant. This is not to generalize that this is the case for everyone in these spaces, I am friends with nerdy-people on an individual basis, but I am painfully aware that I don't fit in perfectly like the last piece of a jigsaw puzzle -- and increasingly have less of a desire to do so.
So for me at least this is not offence, but in addition to the above also some kind of reminder that there is a fundamental rift in how decency and intersocial relations are imagined between the people who share my interests and me, which does bother me. Having that cat-girl appear every time I open some site reminds me of this fact.
Does any of this make sense? The way you and others phrase objections to the objections makes it seem like anyone who dislikes this is some obsessive or bigoted weirdo, which I hope I don't make the impression of. (Hit me up, even privately off-HN if anyone wants to chat about this, especially if you disagree with me, this is a topic that I find interesting and want to better understand!)
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Thank you for putting into words what I could not. "Nerd culture" has fallen a long way since the early 2000s and your quote about decency and intersocial relations spoke to me.
It is really bizarre how everybody tries to make it about politics. While I may or may not disagree with a developer's politics, it's their conduct that I care about, and I associate those who express appreciation for anime at every possible opportunity with especially poor conduct and have yet to have encounter an exception to the rule.
The amount of flags I'm seeing for posts simply expressing disagreement on the matter is quite worrying.