@lalah

For the serious answer...

Zeon attacked their homes and they're kids who grew up with the Principality of Zeon as a villain. That's like asking why kids who grew up during the Cold War were rarely supportive of communism even though capitalism was often a really raw deal even then.

Bright, on the other hand, probably understands the situation well enough to get that while the Federation is corrupt and elitist, it's better than Zeon's monarchism, nepotism, and authoritarianism which killed millions of civilians in a colony drop at the start of the year. He's also aiming to be a military officer in the first place, so there's probably some loyalty implicit from being admitted to that program as well.