Why dooes Nitrogen reacts with Hydrogen to make ammonia

In covalent bonding, to make a stable molecule, you must fill in the electrons in your valence shell. So why is it Nitrogen reacts with hydrogen to make ammonia when you get a pair of lone electrons? Why does the same happen in water.

It's a matter of formal charge. Look at the structure of ammonia - the nitrogen in surrounded by three single bonds and one lone pair. This satisfies the octet rule - it's valence shell contains 8 electrons, shared or unshared. Why doesn't it want four single bonds?

Formal Charge = (# of valence electrons on neutral atom) - (# of bonds) - 2(# of lone pairs)
Nitrogen has 5 valence electrons on its neutral atom, so 3 bonds and 1 lone pair leave it with a formal charge of zero, which every atom wants. Four bonds would leave it with a formal charge of +1 - and the only thing an electronegative atom trends towards less than neutral formal charge is positive formal charge.

The same is true in water - the oxygen usually has 6, then you subtract the two single bonds and the 4 electrons in lone pairs, and you get zero. Everything loves zero formal charge.