I don't do it => I don't do it/I don't participate in it/I don't practice it/I don't believe in it. That person doesn't like romance and therefore doesn't do anything related to romance. Historical note: The expression "I don't do something" came from a very old Windex (window cleaning liquid) TV commercial where a snooty maid told her prospective employer, "I don't do windows", meaning she wouldn't clean windows as part of her duties. That commercial made it popular to say things like "Let's do lunch" and "I don't do romance", for example.

This is one of those examples wherein native speakers of a language play a part in the evolution of little nuanced meanings embedded in sentence structures, colloquialisms, double meanings and so forth. It's really amazing to observe. "I don't do romance" means that the person who is making the statement is wholly uninterested in the expected social norms of dating, wining and dining, developing emotional intimacy or love. "I don't do (whatever)" means I'm not willing to engage in whatever it is. It connotes an unwillingness and not generally an inability. On the other hand, "I'm not romantic" might be said by someone who is interested but not very skilled at being romantic.

I think this is a composed expression, it is better to interpret as a whole and not word by word. I don´t do sports .. meaning that you are not interested in doing something, probably because you don´t like it.

do = 做 I don't do nice things do = 我不做好/善事 不过中文会在其位惜沉用別的动词来代替 = I don't do windows, do = 洗 I don't do romance, do = 拍拖