Udina believes that humans deserve a Council seat and they should have it sooner rather than later. Initially he pushes hard for a human to be inducted into the Spectres, hoping that this will be the first step. He blames Shepard for the 'failed' mission at Eden Prime, fretting it might have cost them humanity's best candidate for the Spectres.
During the hearing against Saren Arterius, Udina realizes it was a mistake to bring Captain Anderson into the hearing, as their past history complicates things and Saren is cleared of the charges. He gets Anderson off the case and directs Shepard to meet Harkin for clues to exposing Saren. Once Shepard has become a Spectre, Udina's diligence manifests itself as a preference for playing things safe to look good in front of the Council. He doesn't even bother to thank Shepard for exposing Saren as a traitor.