How does HB contradict the idea of human equality? Also, how can you defend the idea, despite what happens in the story?
One of the main themes of Vonnegut's story is the inherent contradiction in any assumption of human equality. He does not necessarily suggest that one human is more valuable or inherently of greater worth than another, but he does suggest that people have different abilities and different strengths.
If you were attempting to defend the idea of equality after reading the story or going along with the story, you would likely focus on the fact that the various handicaps appear to be placed on everyone. Of course some handicaps appear more onerous than others, but just because some people appear to be physically more gifted or mentally more gifted doesn't mean that on another level there is a kind of equality. But it does not mean that all humans can achieve the same results in the same arena.
A person who is 4' tall cannot achieve the same results in the NBA as someone 7' tall, but the celebration of physical prowess is arbitrary and does not mean that both people are not equal in some other sense.