Under the reserve clause, why and how could teams "own" players?

Under the reserve clause, teams could "own" players
because that is what the contracts said.  The reserve clause was a clause in every
contract signed by professional baseball players.  It stated that the team held the
player's rights even after the term of the contract had elapsed.  The player's only
options would be A) to sign another contract with the same club, B) to ask the club to
release or trade him or C) to stop playing.

As to why this
was allowed, that is more difficult.  The reserve clause was, one can argue, allowed
because of the idea that baseball (and other sports) were just games and that the
athletes should be grateful just to have the chance to play.  One can argue that it was
also allowed because players had so much less leverage than owners
did.