This person is entirely overreacting to Akame ga Kill. Let's take a look:
Yes anime overall has problems with sexism. Yes Akame ga Kill has some sexist issues (male self insert character, fanservice, and some harem elements). But being hyperbolic and hypocritical over a show that's far better than most in terms of sexism doesn't do your arguments any favor.
On the one hand it doesn't matter if the female assassins are capable and rescue the male lead, even though "that is important as a signifier of how progressive something is or isn't" ? Sounds to me like she's already made her mind up about the issue. The thing is, this is probably one of the most important ways that AgK is quite progressive. In virtually all harems the male lead always goes around solving women's problems, and then they fall in love with him. White-knighting fedora fantasy logic at its finest. In AgK, the female (and male) assassins are usually put above Tatsumi by virtue of being stronger, more experienced, and more senior to him. Instead of the uber male coming in and saving all the helpless women, they're always having to help him out and worry about him getting killed. Definitely not sexist in that respect.
So there's fanservice in anime. Yeah, it's annoying, but what do you expect. Still, it's hardly the worst fanservice I've seen, and there's plenty of fanservice for the ladies as well. And I'd hardly say that they're all characterized as wanting to hop into bed with him; they're mainly characterized as caring about him as a friend and as a new member of their close-knit group. The only clear cut case of someone being romantically interested in him is crazy psycho lady Esdeath. Perhaps I've watched too much harem BS over the years, but the character dynamics in this show are different and far better than the typical harem BS.
She actually does have a good point at the start here. I'd agree that the show has elements of a self insert fantasy where Tatsumi's a somewhat bland everyman so the view can insert himself in his place. And the show does have issues with characterization, but the thing is that this extends to the male and female characters as well. She tries to brush this off by saying that the men are not all characterized like this, but if you think about it they all are as well. Bulat's a fujoshi's wet dream, the other assassin guy's the token perverted nerd, and the evil men are more or less comically evil monsters. So AgK has problems with characterization, but they're equal opportunity problems. Again, she's already made up her mind that the show's sexist and is dismissing anything that doesn't fit that narrative.
Now she's just making stuff up. Justice girl didn't show any romantic interest in Tatsumi beyond playing nice friendly cop before showing the audience her psycho side. Again, she's reading too far into the show, and automatically assuming the worst.
Again, misinterpreting events. I'd hardly say that Esdeath's heart was "melted," or that it was solely his fighting ability that drew her to him. I find the whole thing disturbing as well, because it's a "crazy psycho decides to sexually dominate weaker person" situation. In fact, it would be just as disturbing if not more so if the genders were flipped the other way around. And once more she's already made up her mind and is automatically assuming the absolute worst will happen in the show.
Yes anime overall has problems with sexism. Yes Akame ga Kill has some sexist issues (male self insert character, fanservice, and some harem elements). But being hyperbolic and hypocritical over a show that's far better than most in terms of sexism doesn't do your arguments any favor.
