Criticism of feminism and anti-feminism are two different things.
Feminism does self-criticize. Like any movement, it needs to continually evaluate its effectiveness and evolve. That's why we've had "waves" of feminism. Feminists should continually "examine their privilege". Everyone has privileges. Some have more. Some privileges are more significant than others. Feminism is about letting everyone have a fair go but recognizing that women can't help that happen for others unless women in general catch up and the most powerful women have the same influence that the most powerful men do. In the same way, women can't catch up if they leave some women, such as Women of Color, behind. And Women of Color can't catch up if Men of Color can't. Feminists who don't recognize this are not building an effective feminist movement.
Anti-feminism wants feminism abolished. It doesn't want it to change, it wants it gone. Why? Because it's disrupting the status quo and thus it's not about putting men first. Sometimes they want feminism abolished because it's encouraging women to seek and keep careers that aren't "housewife" and "parent" and thus men will have to do more (or anything) in those areas. Other times it's more nefarious and centered around how assault prevention is costing men a "right". Even women succumb to this ideal. Sometimes it's a form of Stockholm's Syndrome. Sometimes they just have good lives and they are convinced they will be forced to change by becoming the exception to the norm.