It isn't whether something can fly that givies it classification as a bird, and the ostrich is not the only kind of bird that doesn't fly.
It is classified as a bird because of its inherent characteristics. Birds follow mammals as the second most advanced form of animal life, and they are split into two types: Carinatae which have keeled breast-bones and the power of flight; and Ratitae which have raft-like breast bones and can't fly.
birds have feathers - penguins, emus, ostrich, rhea, kiwi, road runner are all birds that have feathers but can't fly.
Big Bird (seasame streeet) is not a bird though!