I do not accept the alternative, but I reject the null

We learn in our introductory statistics course to never say, "I accept the alternative hypothesis."  To do so is heresy.  Yet we are allowed to say, "I reject the null hypothesis," and typically, only the null and alternative hypotheses are present, and to reject one would seem to accept another.

I always assumed this is because we can calculate the probability of a Type I Error but not a Type II, but it may be deeper than that.  It may rest in Karl Popper's Falsification Theory, asserts that no matter how many theories we reject, if we are left with one theory that hasn't been rejected, we should never say that theory is accepted, because another theory may arise which also is not rejected.

No theory should ever be called our "best guess," Popper asserts.  Too bad, because we do it all the time.