I agree this isn't a row. In a row, you disagree, there is argument/discussion on both sides..what my old boss used to call 'a full and frank exchange of views'
This just sounds like him insulting you, and you having to put up with it.
Please dont think this is happening because you aren't assertive. It's happening because he is frankly a bit of an arse. The problem is very much his not yours.
Just as an example of why being assertive isnt necessarily the answer...I am an assertive person. I argue back. My Ex - who used to call me a stupid, lazy bitch and lots of other, worse stuff, couldn't handle being argued with, so used to threaten violence, and when that didnt work, would lash out - smashing up my things, and eventually progressing to hitting me.
So take it from me, being assertive and/or 'standing up for yourself' doesnt make the problems go away. A crap man is still crap however you treat him. I think you just need to decide whether being with someone who makes you tread on eggshells all the time, and who you cant stand sometimes, is really what you want.