This leads directly to falsifiability as the organized process of 'doubting' in science. A hypothesis must be falsifiable to be considered scientific, because without meeting that criterium, there exist no objective mechanisms with which to address doubt.
It is not a question of doubting evolution per se, but rather phrasing evolutionary inferences in ways that permit them to be tested. Not every inference made by evolutionary theorists is going to be correct in every particular context, but a correctly framed hypothesis warrants the effort to disprove it - an incorrectly framed one does not. Sometimes you learn as much by disproving a hypothesis as by proving it, but only when it is a 'good' scientific hyptothesis.