Half white and half Mexican. Do I count?

So my best friend and I were on FT the other day and her boyfriend (Mexican) was there while we were talking. Anyway, somehow the topic of Mexico came up and I agreed with him on something he said and he immediately shut me down, said I was white and so I couldn’t say anything. We were literally just talking about the way Mexico looks (I’ve visited many times to stay with family) and so it wasn’t like I didn’t know what he was talking about. My friend said “she’s half white, her moms side of the family is Mexican.” (My mom is Mexican and so is all of my family on her side) And he said “so she’s white.” Then he walked away and said something. I couldn’t hear him so I just ignored it until my best friend said “did you hear what he said? He called you a racial slur.”

I’ve always loved my culture but I hate that I feel I can’t because I’m half white. Do I count? Am I “diluted”? It really upset me because I’m always so happy to share the culture with other people and now I feel like I can’t.