This is the first time I'm reading (and "hearing") the phrase "bothsiderism" :) I love it! Definitely bothsidering to use it from now on!
As I understand it "bothsiderism" is the practice of not taking a stance for either side of an argument and saying "both sides have valid arguments"/"both sides are equaly wrong", and in the process ignoring that one side is much more right/wrong than the other.
> I think there's blame on both sides, you look at, you look at both sides, I think there's blame on both side, and I have no doubt about it, and you don't have any doubt about it either.
- Donald Trump after violence at the Charlottesville rally