Why is armor more expensive than magic resist?

Because AP is cheaper, protecting yourself from abilities that scale on AP should be cheaper too, otherwise AP scaling champions would be stronger than AD scaling champions for no reason

Also magic pen is flat, lethality scales with levels. This means that you need more armour later in the game when you have more gold when building vs lethality. When building vs magic pen, you need MR earlier when you have less gold. Otherwise leads vs AP champions would feel weaker than leads over AD champions

There's more physical damage in the game.

Towers do AD damage, so you are building defenses against champions AND towers instead of just champions.

Quite the opposite actually;

Armor is cheaper than MR.

Support items excluded:

- 1100 - 2500 (Also has MR) - 2700 - 2700 - 2650 - 2650 - 2700 (Also has MR) - 2800 - 2900

vs

- 1100 - 2800 - 2800 - 3000 - 3250 - 3600 - 3000