Why does Oberon want the changeling boy?
Oberon wants the changeling boy for a few reasons. First I would say he is most likely trying to find an excuse to argue with Titania and trying to hurt her. The boy is the child of one of her followers. His mother was a close companion of Titania and died while she was giving birth. Titania feels that raising the child is her responsibility.
I think there is a more subtle reading of why Oberon wants the boy though. Eventually the argument becomes as such: the boy will have no male role models, as Titania's servants are mostly women. Titania fawns over him, putting flowers in his hair and this greatly upsets Oberon. So for the sake of masculinity, Oberon wants the child.
At the beginning of Act II, Oberon, King of the Faeries, and his wife Titania are arguing over a boy. Titania has gone to India and taken this boy for her own after his mother died. She claims him because the boy's mother was one of Titania's devotees.
Oberon just wants the boy because the boy is very "beautiful." For whatever reason, that makes him want the boy to be a "knight of his train." This means that he wants the boy to be one of his followers.
It appears that Oberon and Titania are just using the boy as an excuse to quarrel.