How did James II anger English parliament?

Largely by existing, it seems. There was an unfortunate tendency during that era for monarchs to believe the proper role of Parliament was to do whatever the monarch told them to do and for Parliament to believe the proper role of the monarch was to pose for stamps and coins, and eventually produce an heir, and to otherwise shut up and stay out of the way.

In James' case, one problem was that the produced heir was Catholic (as was James himself, which didn't exactly make him top of the pops either).

If you want a more specific answer, you'll need to ask a more specific question.