Is it normal for someone to fail a couple of classes in their major in the first two years of college?

If you're failing classes in your intended major, you really should rethink your major or school all together. Are you failing because it's too hard for you, or because you're uninterested in the subject, or because you're uninterested in college in general? If it's college in general, stop wasting yours and/or your parents' money and take a break until you're ready to be serious with school. If it's that the classes are too hard, look into more remedial classes to prepare you for the tougher courses or reconsider your major entirely. If you're finding the classes completely uninteresting, then it's definitly time to switch majors. In short, no, it's not normal to fail classes.