Because they had signed on to an agreement that tied their fortunes to the Union, an agreement which has no provision for withdrawal.
The Declaration of Independence argues that the "Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness." is a fundamental right. Can you sign your fundamental rights away? Isn't that a little like slavery?
I will point out also that the British Colonists were expected (required by law) to show perpetual allegiance to the King. We see how that turned out.