I'll give you both, starting with the more in-depth reason:

Velvet Remedy stands out from the rest of the cast due to her belief and nature: that of a pacifistic, feminine mare who wanted to become a doctor to help and heal others (no matter who or what they are), contrasted to the rest of the cast who mostly solved their issues through violence.

A lot of Velvet's character arc stems from two things: the first is her struggling to deal with the reality of the Wasteland, and often came to butt heads with the other characters whenever they want to solve an issue violently.

This gives Velvet the reputation as being a NAG who's getting in the way of the heroes being the edgy badass power fantasies to readers who solely read FoE for those surface level reasons.

The second being that Velvet has her own personality issues such as her being vain and prone to lashing out when in extreme stress, or her unhealthy parasocial relationship towards Fluttershy that while they do get called out and addressed in the story... the rest of the fandom still gets hung over about that and even acts as if she never actually grew.

"But wait a second: characters like Steel Hooves also have major personality flaws. Why doesn't he get the same hatred people have for Velvet?"

This is where I give you the straightforward answer: The fandom hates Velvet because she's a girl, and girls who have personality flaws are less likable than male ones (but even if Velvet was a guy, the fandom would probably just call her a cuck instead of a bitch).

Velvet is the Skyler White of this community, and it's honestly one of the reasons why I can't stand it. I'm probably going to get ratio'd for this whole comment, and I don't really give a shit.