Did I take it too far?

I 27(f) am biracial (white/black). My bf 27(m) is black. Last Sunday he kept nit picking for about 2 hours and it was super annoying. Towards the end of his nit picking/playing, I asked him if he could pass me the chips sitting next to him and he said “these are for real n***** only - you half breed.” Usually this wouldn’t have bothered me but this particular week we had had several conversations about my biracialility and how it’s impacted my life and I felt like the timing was… insensitive. In response I said “well what if I said you had a small d” to which he shrugged off because he knows it’s not true. But the message or point I was trying to convey was that it’s not fun to poke at insecurities people can’t control. Then I said “well what if I said you had a pencil d?” ( Which in full disclosure I don’t think) but I went with the next logical projection from short d*** to slim d*** and this seemed to hit a nerve. Long story short he hasn’t really talked to me since Sunday and told me I have “turned him off.” But I guess my question is - am I in the wrong? Was my reaction to his action too harsh? I’ve already apologized but I feel like he is dragging this out unnecessarily and trying to stand on moral high ground but I feel like we wouldn’t be in this predicament if he hadn’t called me a half breed?