Why does oberon want the changeling boy and why does Titania?
The first mention of the changeling boy is Puck who says,
For Oberon is passing fell and wroth
Because that she, as her attendant, hath
A lovely changeling boy stol'n from an Indian king.
She never had so sweet a changeling:
And jealous Oberon would have the child
Knight of his train to trace the forests wild.
Titania is the next to talk about him when she refuses to give him to Oberon. Speaking about the boy's mother, she say, "...her womb then rich with my young squire,..."
Oberon is the last to make a heraldic reference when he say, "I'll make her render up her page to me."
It would appear from these references that Puck is referring to the future of the changeling boy, to be knight.
Titania it would seem is referring to the next step for the young boy's progression toward knighthood, that of being a squire where the young boy leaves the company of women to learn the skills necessary to become a knight.
Oberon is referring to his current position as a page since pages were the first step in becoming a knight and they would attend the women and learn the gentle arts from them.
It would appear that Oberon wants the changeling boy because it is time for him to leave the world of women and join the world of men.