They're not "claiming" anything you gave them governance rights.
Nope, I certainly didn't. You see, in my view, I don't have the right to govern anyone but myself. And that's not a right I've delegated to anyone else.
but there is nothing inherently coercive about representative government.
Sure, apart from maintaining mass, systematic, threats of violence against peaceful people, backed ultimately by the willingness of government agents to use deadly force, there's nothing at all coercive about it [eyeroll].
What I meant was: every member of a village invests one dollar into a fund used to fund private militias, only five people are competent enough to invest appropriately, so they effectively end up with the "right" to enforce militaristic governance.
It's a crude example but should get my point across. The idea was just to show how it evolves out of collective consensus.
Imagine every member of a population were appropriately represented in government. And they all agreed that a select group of people could punish them, whenever certain rules were broken. Would you consider that coercive?
Have they voluntarily entered an explicit contract with the rulers (while not under duress by those same rulers)? No citizen in the world right now has. If not, it's coercion - and more importantly a rights violation by the 'rulers' against the 'ruled'.