Can someone fire you if they do not like you?

Unfortunately it's a reason that people often get fired, it's something that happens when someone in power has biases, some people are probably going to get more chances than others if you see what I mean or you might get dropped for having "a bad work ethic/attitude" or whatever.

Even though it really shouldn't happen, remember it's always easier to think "paul fired me because he hates me" instead of "paul fired me because I was late too often".

Every case is different.