It is going back a bit, but I feel I neglected a comment by Amos, when we were saying scientific experiments were set up to disprove the null hypothesis. Amos said:

An experiment that DISPROVES the null hypothesis supports some alternative hypothesis, n'est-ce pas?

And that's perfectly true. So why the apparent awkwardness of disproving rather than proving?

It's best considered via an example. Suppose I wanted to prove the statement 'All crows are black'. Basically, it can't be done. I may have examined a million, or one hundred million, crows but I can never be certain that if I go over the next hill I won't come across some white ones. So no matter how many 'agreements' I get, I can't be certain whether the hypothesis is correct or not.

Now suppose the opposite: After examining a bunch of crows I come across a white one. Job done: the hypothesis is disproved, no uncertainty.

And that in short is why experiments are set up to disprove, rather than prove.