Is this grounds to break up?

I've been dating this guy for about 3 months. Sometimes he makes a lot of sarcastic remarks directed towards me. The other night I told him I had a song stuck in my head and that's because I have "too much space in there." There have been other sarcastic remarks directed at me as well. Also the other night when I was talking to him about trying to find a new exercise routine he responds because I'm tired of jogging he says "I don't know what to tell ya" and drops it. He also is not open about his feelings but then says don't mistake his coldness for not caring. Should I break up with him or am I just making too big of a deal out of it. He does do nice things like taking me out or just spending time going for a walk or watching a movie, which means a lot.