When the Battle of Hogwarts arrived, Anthony fought because it was the right thing to do, not because he believed in the cause.
No, he certainly didn't believe that Voldemort and his minions were right. He despised the way they slaughtered Muggles, Muggle-borns, blood traitors, and anyone else who disagreed with them as much as anyone else did. What he didn't believe was that people with such differences could live relatively peacefully together.
Anthony Goldstein's identity is made up of halves. He is a half-blood—witch mother, Muggle father. He is half-Christian and half-Jewish. His name indicates his bi-religious heritage: Anthony is the name of a Christian saint, chosen by his mother, while Goldstein is his father's name, a common Jewish surname.
His father used to tell him that he would be the bridge between two worlds. Anthony, however, thinks that it isn't possible to bridge two worlds; there is always a gap between them. The best that can happen is a few bold individuals live with one foot in each. That option is not available to Anthony, however, because he is the gap.
All his life Anthony has found himself ostracized for being half of each world. Half Muggle, half wizard, half Christian, half Jewish, half everything. He hates feeling permanently cleaved in two, and condemned to stay that way. So he decides that he's not going to try to reunite two worlds. If the inhabitants of each are living in peace with their own kind, and everyone is happy, why bother?
This attitude sustains him throughout his years at Hogwarts. He lives in the gap, the void between two worlds. He's permanently stuck in a ravine, in a crevice. On each side of him is a view high up of one of the two worlds he is caught between—a distant paradise that will never be his. And he's fine with that. He knows his place in the world, and everyone else is happy with where he is. Why should he interfere with the harmony of the world?
It is only after the Battle, when he sees that there are many other people who also live in crevices, that he realizes his folly. The mistake of a lifetime. It's impossible to unite two worlds—which is exactly why you must unite them. World harmony doesn't come from human beings isolating themselves and living in their own little villages. World harmony can exist only when people can set aside their differences and live with each other.
Anthony can't climb out of his crevice. Not right away. The lifetime he's spent moping in his own little fissure has left him buried so deep it takes years of patience to climb back out. Once he's climbed out, he has to learn how to bring the two worlds together. To unite the two shores never meant to unite.
But try he does. For the only life he will accept is in a world in which all worlds coexist peacefully. Not in a crevice.