I see Teela simply as the daughter of Man-At-Arms. Her mother died unexpectedly when Teela was young, and Man-At-Arms brought her up the only way he knew how, as an Eternian defender.

The snake armor is just something passed down generation to generation for the bravest female warrior in Eternia.

I also think the Sorceress believes Teela is important in the grand scheme (defender of Grayskull and possible future wife to He-Man). The Sorceress always seemed kinda like a nun to me, dedicated to the mission, but does care for Teela like a mother to a child, like a nun would care for a young girl/ lady trying to do good in the world. My canon is pretty blah and hokey, but I don't see why Teela needs to be a hatchling, clone, future Sorceress, or destiny's child.