why the rich should pay more

Taken from a purely Market Capitalist perspective:

Because they have the strongest interest in keeping things the way they are.

Sure, in practice, taxes pay for defense, roads, welfare, police, etc. In principle, what this amounts to is the stability of a system. Without a system, we would quickly devolve into a far less economically efficient situation. Those with little income or assets would have little to lose from this change - and some of them would inevitably come out better. The rich and powerful, though, would almost universally become less rich and less powerful.

This principle even works on a marginal basis. If taxes are too low and social welfare program become ineffective, inequality of income and crime will rise - leading to the kidnapping of rich family members that we see in areas with high income disparity and no social welfare. For most, the cost of increased personal and family security would be greater than the cost of increased taxes.

This is such an obvious fact, that I doubt many wealthy people who have actually taken a moment to consider the implications seriously believe that their tax burden should be low.