There is no "in universe" answer. He didn't get a metal because Mayhew was so tall, it would just look silly to have him bow down so low or Leia to climb somewhere and look awkward. For film reasons, it would have interfered with the flow of the story. Also, Chewie's character grew over the course of the films, and maybe he wasn't intended on being more than a pet originally and we all see the SW universe discriminates, especially against droids.
With all that said, the expanded universe explanation is that Chewie rejected the metal because his culture does not believe in being honored for tasks they see as obligitory, in this case, helping and being at Han's side. Marvel had him get the award after the ceremony when Leia could climb atop a table (see dbalschi's photo).