What allowed the Himalaya to become so high?
It mostly has to do with the type of convergent boundary the  Himalayas are, continental crust to continental crust. Most convergent boundaries are oceanic to continental or oceanic to oceanic. In both cases there is a dense oceanic plate that can get subducted. But in a continental crust to continental crust collision neither can really dive under the other and get reworked*, since both are low density, thick, and roughly equal in density, so they just compress together like pushing two wads of clay together. They build both up and down since they sort of float on the rock below. Think of it kinda like a geologic iceberg, it is too light to sink. All compressive collisions  thicken like this to a lesser extent, due to the compressive forces, it is just far more intense with continental to continental collisions because there is no other outlet for the energy but compression because all the material involved is to light to be subducted. . 

the Eurasian and Indian plates are both large continental plates so as long as they are getting forced together they can only get thicker and thicker. This is the only boundary like this on earth right now, so it seems weird to us, but this type of collision has happened before they are just rarer. 

*sometimes one does go down more than the other but it does not get reworked, they just get fused together in a lopsided fashion.