Why is the null hypothesis usually the no-change statement instead of the claim I want to prove?

The null is the claim that remains in place unless the sample evidence is strong enough to reject it. That is why it usually states equality, no change, no difference, or no effect. The alternative is the claim that needs evidence.

If an analyst says a signal increases expected monthly return above 0.50 percent, the null is that expected return is less than or equal to 0.50 percent. The alternative is that expected return is greater than 0.50 percent. The test asks whether the sample result is far enough above the baseline to justify rejecting the null. This setup controls the risk of treating random sample noise as proof of improvement.