if you really want to record something on your mac I guess you could use QuickTime Player (most macs have it by default I think)
I have no idea if it is good or not but it should be acceptable, I actually don't know where your recordings go but I believe you have the option to upload them to youtube at least.
If you don't have QuickTime Player already I guess you could check if it is free, if the program isn't good enough for you or it isn't free...Well then you might have a problem.
Edit: obs isn't really linked with twitch, it allows you to save recordings directly on your computer or stream through streaming services, twitch being one of them.
Edit2: obs has a version that should work for Mac, called OBS Studio.