and if you wrote a very good paper, and he's not a pompous ass, it should be okay.

If the college operates under the academic tradition, the quality of your work will determine your future regardless of the conclusion about the method. Sadly, many colleges have been infected by the corporate model which favors suck-ups, yes-men and sycophants. If it is, toss your 40-page paper and submit a 5-slide PowerPoint titled "Boss Method -- Good!"

Professors usually appreciate constructive criticism, your criticism was constructive right?

If he can't handle the criticism, he shouldn't have written anything that could be worthy of arguing or criticizing. I wouldn't worry. That's how it works in the real world. Everybody has something to say about somebody else's work.

Time for a new essay?

I think as long as you don't have snide undertones in your paper you'll be okay. Maybe edit to make sure it's accurate and fair to both sides. He might appreciate a good debate.

So you're passionate about a subject he's passionate about too. That's great. If the paper was any good, this is probably a good thing.

I had a professor who would listen intently to our agruements. Even the ones that argued aganist his theories. When we were done, he would say, great agruement, valid points, but you're wrong and here's why. I think you'll be fine.

As long as you didn't get personal about it (and I doubt you did!), if s/he's reasonable, s/he'll probably appreciate it, or be neutral at worst. Any academic who publishes understands their work will be criticized, especially if it's on a global stage. Part of the whole idea of thesis defense is learning to deal with people questioning your ideas. Who knows? Maybe you'll have a good talk about it!

If your criticisms are valid, thought through and positive in the manner that you present your findings, you shouldn't have any issue. However I'd be sure it is complete and you aren't missing anything. You don't want the professor to destroy your paper and validate their method.