Why do we add objects to some but not to others? How do we know that it's an object and not a modifier?

I still don't fully understand why it cannot be A. Both support sentences support the statement. C says pretty much the same thing but adds on the spareness. I've listened to multiple explanations and it just isn't clicking, anyone have a good explanation that helped it click for you?

Hi! I am in a similar position as you and would love to study together! Message me if you're still looking since this was posted a few months ago now.

Hi I am in Portland Oregon, would love to study together at some point. I am not as far along as you in my studying though if that makes a difference. Message me if you're still looking!