I suspect its because you don't understand the purpose of the university. LDS faithful saying that they hate or disagree with the university make no sense to me. It is the school of the church and quite frankly has the official support of the Prophet, First Presidency and Quorum of the 12. You don't necessarily need to be a fan of the sports teams, or you can be a bigger fan of another team - but to actually hate the university - I think that is worse than lame.

As for BYU doing things that reflect poorly on the church - No it doesn't. Some of the people there might, but nothing official about the school does.