Movie stands as condemnation of 'fate'

As you suspect from the beginning, and find out at the end, they belong together. I don't say "belong" in a supernatural, "fate" sense of the word, but in the sense that they actually want to be together. However, because she believes in fate, they spend several years (in the prime of their lives) apart, and in unfulfilling relationships. Those years are, to a certain extent, wasted. Life is short, and you only get one chance.

Some might argue that they needed that time apart to learn something, or to realise they are really meant to be together. There's no evidence to support this claim; they had an immediate attraction, he knew he wanted her, she at least suspected that she wanted him. If they had just dated for a while, they would have found out for sure. Now some will say "but then there wouldn't have been a movie", or words to that effect. This is also not true, they just would have had to write the movie better than they did.

On a more general topic, for you fate believers out there, take a moment and try to rationalise how "fate" could possibly manifest itself in the real world. It's fun to fantasize about stuff like this, and watch movies about it, but if you actually base life decisions on it then you're doing yourself a massive disservice.