Another reason police unions are entirely different, even from other public sector unions, is that the police are used to break strikes. They're structurally antagonistic to every other part of the labour movement.
This is right, but the national guard are often used as well. I alluded to these points in a comment below before noticing that you posted this first.
I would caveat it to say they are used to break illegal strikes, which I think is an important distinction. Their job is to uphold the law, regardless of the side that labor is aligned.
