Martial arts are a sport and a game of skill. It's no coincidence that people who do judo and various types of jiu jitsu are described as players and that submission grappling is sometimes described as human chess. Rather than thinking of it as a "fight", try thinking of it as a test of skill and technique. If you get hit or someone blocks one of your strikes, consider that to be something to work on. Conversely, if you hit them successfully or block one of their strikes, that's a success. I'm not particularly aggressive but I got my BJJ blue belt a couple of months back because as part of my technique I look for weak spots and mistakes while trying not to give anything up myself. When I do Thai sparring I sometimes try a few different styles just to see what works against someone. Sometimes with BJJ I'll deliberately put myself in a weak position or allow someone to set up a submission to see if I can work out how to get out of it.

Part of the training is getting used to being hit or having someone sitting on you while trying to decide what to do next. A lot of it is down to experience. I'll sometimes allow someone to start putting on an arm bar or triangle choke because I've got a couple of escapes that I know work quite effectively and put me in a dominant position afterwards.