I agree with pretty much everything. But... without more information it's impossible to really comment constructively. I'm very, very good at what I do. Not bragging, just a fact. I am strong. I am assertive. I am a good leader and a strong mentor. Etc. Etc. And I can be abrasive! Sometimes "abrasive" is actually the right thing. Sometimes I misjudge, and it isn't. Sometimes I just get frustrated or annoyed and "abrasive" pops up, deliberately or not. Often not, although fortunately not all that commonly now.
Abrasive can be a good thing. Sometimes it's a matter of judgement. And I don't see it as gender /sex based without a context - I've met many abrasive men.
And every now and then I'm deliberately abrasive because I really, really don't like you...
You need to understand what the context of the comment is, and don't just ignore it. Abrasive is neither good nor bad - it's all down to how you use it, or it uses you. So don't throw the baby out with the bath water. One way or another there is learning.