Why can't we accept the null hypothesis, but we can accept the alternative hypothesis? I understand it's reasonable only to not reject the null hypothesis. But why can we accept the alternative hypothesis?
What's the difference?

Say you have the hypothesis

"on stackexchange there is not yet an answer to my question"

When you randomly sample 1000 questions then you might find zero answers. Based on this, can you 'accept' the null hypothesis?

You can read about this among many older questions and answers, for instance:

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*Why do statisticians say a non-significant result means "you can't reject the null" as opposed to accepting the null hypothesis?

*Why do we need alternative hypothesis?

*Is it possible to accept the alternative hypothesis?
Also check out the questions about two one-sided tests (TOST) which is about formulating the statement behind a null hypothesis in a way such that it can be a statement that you can potentially 'accept'.

More seriously, a problem with the question is that it is unclear. What does 'accept' actually mean?
And also, it is a loaded question. It asks for something that is not true. Like 'why is it that the earth is flat, but the moon is round?'.
There is no 'acceptance' of an alternative theory. Or at least, when we 'accept' some alternative hypothesis then either:

*

*Hypothesis testing: the alternative theory is extremely broad and reads as 'something else than the null hypothesis is true'. Whatever this 'something else' means, that is left open. There is no 'acceptance' of a particular theory. See also: https://en.m.wikipedia.org/wiki/Falsifiability

*Expression of significance: or 'acceptance' means that we observed an effect, and consider it as a 'significant' effect. There is no literal 'acceptance' of some theory/hypothesis here. There is just the consideration that we found that the data shows there is some effect and it is significantly different from a case when to there would be zero effect. Whether this means that the alternative theory should be accepted, that is not explicitly stated and should also not be assumed implicitly. The alternative hypothesis (related to the effect) works for the present data, but that is different from being accepted, (it just has not been rejected yet).

