If someone accuses you of being assuming, he or she thinks you are arrogant or that you take too much for granted. If you take on an assuming tone when you ask for something, people are more likely to feel offended than to be generous.
A person who is quiet and modest is often described approvingly as being unassuming. That person's conceited cousin, with an inflated opinion of himself and a strong sense of entitlement, is more of an assuming sort. You can also use this word as a conjunction. Assuming we leave at 9:00 a.m. and there is little traffic, we should arrive in the late afternoon.