It's not about challenging the results of the election. I mean, not in that sense. Regardless of whatever else you want to say about the election, Trump has said and done some pretty nasty things, and people are frustrated because his election means the validation of those things. People are protesting the hate and the sexual assault allegations and making fun of disabled people, and letting everyone know that we don't think that those things are ok. Not that the results of the election should be reversed. I'd like to think nobody in this discussion or on this forum advocates mocking a disabled person. Trump did that once. Protesters/rioters/whatever you want to call them want to show they don't support that behavior.
As for the election recount, there were concerns (although even the Hillary campaign is well aware that few are reasonable) over various forms of voter interference or hacking. Whether it's true or not, there's public outcry, and since the money has been raised to do it, there's no harm in a recount. Again, regardless of whatever side you're on, there's no question it was a divisive election, and both sides are riled up. A recount of votes is pretty mild given that divisiveness (since again, there's no harm--if nothing is found, then nothing changes, and if something is found, then of course it needed to have been found and action will be taken accordingly).
