Should I let him go?

Okay so, this question may sound a bit similar to another one that was on here a while ago because it's pretty much the same situation with a different question. Anyway, I was kind of involved with this guy for a few months. I really liked him and he told me that he liked me so much. He's a good guy but he had a minor issue with one of my parents and ended up being on their bad side. Family means a lot to me and at that time, I was going through some stressful stuff so, the tension between he & my family put me over the top. I ended things with him. I was hurt and he seemed hurt as well. However, his actions lately have kind of made me wonder. I ran into him one day and held eye contact with me before saying hello. He has somehow managed to be back on good terms with my family. I saw him one day & again he looked me in the eye for a couple of seconds before actually saying hello to me then asked me if I was gonna continue doing some activity that I did before which I always met up with him before going to. Recently, I was with my sister and we ran into him. He just waved hello from afar but she thought it was "weird" how he seemed to have been going out of his way to say hello.

I still like this guy and his actions along with my gut kind of tell me that he still likes me too. I could be wrong but, it's honestly what I feel and think. The problem is that he and I haven't been able to officially talk because our schedules keep getting in the way. I've been patiently trying to find a way or time to talk to him but, my friends think that I should just give up and let it go already. They think that all hope is lost between the two of us and that there's nothing more left to do. My gut, however, tells me that we both still have feelings for each other and should at least try to find a way to discuss this. So, am I being stupid? Are my friends right? Should I just simply let things go or should I should listen to my gut feeling? What would you do?