Is it normal to be irritated by people yet want a strong friendship?

You're right but that is nothing new. We're progressing towards a more socially ethical society so when we have to deal with people that are still lagging in a few quarters it's just such a waste of energy. Education has become so prevalent that many of us now know that there are other options besides negativity and fighting those you don't like, but those that have not gotten the grasp of that are twice as annoying any anyone with more than a couple of brain cells =/ We're going through a period of ethical evolution, it'll take a while.