Why don't gases such as neon and argon combine chemically with other elements?

Answer 1

The rare gases, also known as the noble gases, are a group of six gaseous elements found in small amounts in the atmosphere: helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon.
The low reactivity of the rare gases is due to the arrangement of electrons in the rare gas atoms. The configuration of electrons in these elements makes them very stable and therefore unreactive. The reactivity of any element is due, in part, to how easily it gains or loses electrons, which is necessary for an atom to react with other atoms.
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Answer 2

Since the 1960s, compounds of radon and xenon with fluorides and oxyfluorides have been prepared. Apparently, these gases have a large enough radius that electrons can gain stability bonding with fluoride or oxyfluorides.

Answer 3

They have a full outer shell of electrons that satisfy the octet rule. Since you exchange electons when a reaction takes place, full atoms don't take part because they've had their fill. Basically, they're full so they don't want any more electrons from any other atoms.