But how can you be sure he doesn't do this to all students? (answer facebook emails after he is already late) and that he always responds quickly and easily to other students?

What do you want from him? It doesn't sound like he is going to answer your emails quickly and easily. Who knows why? But, if the problem is that you want a response, then you might have to just keep asking the question? Squeaky wheels do get greased and who knows; other students you talk to may not send emails as often and get "lucky" when they do or they may send a whole lot more emails than you do and not think about it and just say, "yeah, he answers my email" because technically, eventually, he does?

If he doesn't like you and deliberately, with malice aforethought doesn't answer your emails, you still have the problem of having to set up another appointment, so you have to keep asking until you set up another appointment?

I often don't think certain people like me or will think negatively about relations with others but it really just boils down to what do I want; what is the "question"/problem. Yours is not to get him to change/like you but to set up another appointment. Concentrate on that actual task instead of the unpleasant personal possibilities and things (for me, when I do that) aren't as ugly feeling to me. Tasks are just tasks and some are harder or take longer or whatever but they're all doable. Trying to wander through the minefield of human emotions and interactions, on the other hand, sometimes gets me blown up