People are complicated. Some people are born offended - and were probably offended that they had to leave the womb - and some people are not offended by anything and everyone else lies somewhere between these extremes. So, a part of the answer is because some just want to be offended about something.
This is a small part of the answer and for these people I still respect their right to feel offended, even if I don't agree with it. The biggest part of the answer comes from the very human reaction of seeing someone not respecting something that is important to a person. This isn't limited to cultural appropriation. If something is important to you, even something like a specific anime or science fiction book, you get angry when you feel someone else isn't giving it the respect it is due.
In any question of cultural appropriation - and, really, anywhere that power can be gained - I also think dishonest people stoke the flames of hatred for their own personal gain and create/widen fault lines that weren't there before and trivial issues and appropriations that weren't malicious suddenly become a huge issue.