I actually had a difficult time coming up with answers for this one. The male version of this thread was so easy by comparison. I think part of the reason is that there are a lot fewer anime that center around a female protagonist than male and many that do are shoujo romance where the protagonist is mostly inoffensive/uninteresting. I could think of more if we are talking manga where there is just a larger volume and variety of shoujo and josei stories.

I was able to think of a couple that I wasn’t a huge fan of when I was browsing the female protagonist tag on AniList.

• Usagi Tsukino - Sailor Moon - Look, as an older guy, I am not afraid to say I actually like Sailor Moon the show and have seen most of the original series as well as the Crystal remake. However, Usagi can be a not-great protag a lot of the time. She is just insufferably stupid a lot of the time.
• Kagome HIgurashi - Inuyasha - I think my gripes with Kagome really stem to Inuyasha being a bit of a dated show at this point. She is all too often either scolding Inuyasha or being a damsel in distress waiting for him to rescue her. If Kaoru from Kenshin were the protagonist, she would have these same complaints from me.
• Ai Tanabe - Planetes - This one was a big letdown for me because I love so much of this show, and I loved her character for most of it, but the ending of her character’s story in that show is just terrible and I hate it.
• Miyo Saimori - My Happy Marriage - A more recent example. I really liked the first half of this show, but as it went on I felt like it was just a whole lot of wasted potential.

Haruhi: I didn’t like the characterization and being an almost-supernatural being, has no need for character development. Giving her less screentime in the Disappaerance movie noticeably increased my enjoyment of it

The first one to come to mind for me is Emiru from Nozoki Ana. I get that the underlying idea is that she’s broken, but even with that, I just didn’t find her the least bit sympathetic. At all. Ever.

Another that comes to mind would be Hina from Domestic na Kanojo. It’s as if the theme for her character is “someone who consistently makes nothing but the wrong choice.” At every turn, there’s a fairly obvious path she should follow, either for her own good or for the good of others, and it’s pretty much guaranteed that that’s not what she’s going to do. And there’s nothing consistent about her character - for instance, it’s not that she’s capricious and assertive. She just suddenly becomes capricious and assertive when she should be thoughtful and cautious, and then when she actually should be capricious and assertive, she just as suddenly turns thoughtful and cautious.

I’m sure there are more, but that’s all that comes to me at the moment…

Good question, but why is a picture of my waifu on the post?

Not a protagonist really but the woman I hate most in anime is Vivi from One Piece. The most useless character ever.

Obligatory Sakura

But otherwise, Frederica Greenhill. LotGH is a great anime (and Yang is one of my favourite fictional characters), but the entire series has just two memorable female characters - Hilda and Jessica. Frederica gets a lot of screen time, but 99% of the time she’s just there.

Orihime

My vote would be the female lead in Guilty Crown, but mainly hecause everything in that was terrible

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Aqua

Not sure if I’d call her “the worst”, necessarily, but Miaka from Fushigi Yūgi always annoyed the heck out of me. She’s pretty much a canon Mary Sue.