And here's the cause of it all: Duty.Well I don't totally disagree. There should be exemptions available if necessary. I certainly think so. But some would say that it's duty rather than slavery that makes a citizen liable for service.
In many ancient cultures it was the freeman that was liable for military service; not the slave. The slave was not entrusted with weapons.
Why should we owe any duty to king or country? No-one's born a vassal. We're born free and unencumbered by duty or obligation.
What gives any person or organization the right to order me to do something I conscientiously object to?
Duty to anything but principle is fraught with danger. Nationalism and "just following orders" has generated little but misery.
Remember "What if they gave a war and no-one came?" -- That's what would happen if people renounced personal or national duty.