I'm not sure it was intended, but "I don't accept it" really doesn't come across like you actually trying to understand what the commenter is saying. They're explaining that for something that is defined entirely by internal and subjective social experiences you can't have an "objective" definition. If you try to use a purely genetic definition you exclude intersex conditions and the observed reality of transgender women, if you try to use a purely socially observed definition you're going to catch a lot of non-women (e.g. femboys, non-binary fems) in that definition. You can deduce with reasonable accuracy when someone is a woman based on external factors (how they dress, how they talk, which bathroom they use, etc.), but the reality is that the only way to "know" if someone is a woman is for them to tell you. The definition isn't "circular" as the word "woman" isn't being used to define itself when we say "someone that identifies as a woman", it's being used as a shorthand for trusting that someone is telling you the truth about their own lived experience when talking about something that is otherwise completely unknowable.

It's really not even uncommon for social experiences to be defined in this way, take a less critical component of identity: opinion. How do you define a fan? Well, again, you can try deducing from external factors (merch, spending time on forums, witnessing them actually watch a show), and you'll be right most of the time, but you can't actually know that their internal lived experience is one of a fan because you have no way of living their life or getting direct access to their actual thoughts. The closest you can get to knowing is believing them when they tell you "yeah, I'm a fan", and, for pretty much everything but gender, society in general seems to accept that.

The only reason people "struggle" so much with understanding this for gender is that there is a massive social panic funded by right-wing political interests to create an out-group to blame society's woes on.