How do the molecules in the thermosphere emit more radiation than they absorb?

"Solar radiation at the top of the atmosphere is 1367 Watts per square meter which if absorbed by a blackbody gives a maximum temperature of 121C"

That (the vit about 121C) is wrong. The sun basically behaves are a black body with a surface temperature of just under 5800K (around 6200°C very roughly).

This radiation is capable of heating another black body (call this X) up to the same temperarture (6200K).

However, X is also losing energy as it is radiating some of it energy away into space.

When in a steady-state, the actual temperature of X depends of X's rates of aborption and emisssion of energy and X's size and composition.

If X is a complex system (e.g. a planet with an atmosphere) things get very complicated because of the various interacting heat flows through the atmosphere which gives rise to different temperatures through the atmsphere and at the surface.

My comment about the solar isolation at the top of the atmosphere (TOA) coming out as 1367 Watts per sqaure meter corresponding to a maximum temperature of 121C is not in any way incorrect. Your argument that the Sun can heat anything up to its own temperature is not true. The intensity of the radiation emanating from the Sun decreases over a distance and becomes progressively weaker for bodies that are further away. Obviously since planets that are further away are colder. So my question remains unanswered as far as I can see. Once again the Earth is only getting 1367 Watts per square meter which is not enough to heat a body up to the required 2500C.