Am I wrong for getting offended and reacted coldly at my boyfriend for saying I’m unteachable on sports

Me and my boyfriend got into a fight after I asked him if he could teach me to play golf. His response was ‘no’ as he sees me ‘unteachable’ on sports and dont have the body composition for it. I got offended and said he was mean. I didn’t talk to him until he pushed me to share how I’m feeling. I explained to him that I don’t think anyone is unteachable of certain thing, maybe it will take a while but eventually the skill will be learned. I even mentioned that I know some people that I think are on my same body composition that plays golf. He then explained that we already tried playing on golf simulator one time (not even 10 minutes on golf, as we tried other sports) and he sees my coordination skill is just not enough. He said maybe I’ll learn eventually ,slowly, but it will not ideal for everyone in the golf course as I will eat more time with my poor coordination and I don't have a body of a sporty person. He mentioned that he’s saying those things based on facts and not trying to be mean. I then processed his thoughts, said I’m trying to understand his thought and reflecting on it, I still gave him a cold treatment as that’s how I react when I’m offended. He got mad because he didn’t like how I process our discussion and insisted me to talk more. I told him that I feel like I have said enough and just hard to process the reality.

Am I wrong with how I reacted on this argument.