Is it normal/okay if my professor grades me lower "in comparison to my peers"?
Sounds like you're in a course which is grading on a curve. The idea here is that everyone's score is going to fit a Bell curve with a predetermined mean. This means there won't be any "Christmas-comes-early" results where everyone scores A's, but also no "what-the-hell-everyone-is-failing" panic attacks either. Grade inflation is unlikely in a class that's grading on a curve, because there'll only be so many students who get A's.

If you're in a class which is grading on a curve, then yes: it's normal to "deduct points" because someone wrote better than you. "Deduct points" in inverted commas because you don't actually lose points, you just get a lower grade.

If you want to score well in such a class, you'll need to outperform your classmates.