Why don't we breathe nitrogen when it makes up most of the air? Why don't we breathe nitrogen while it makes most of the air? Why do we always tend to breathe oxygen, not hydrogen and nitrogen?

I'd argue that we do "breathe" all those gases. Air that we inhale (at sea level) is about 78% N$_2$, 20.9% O$_2$, 1% argon, and smaller percentages of CO$_2$, neon, methane, etc. So all those gases are going into the lungs with every breath in.

We take up oxygen preferentially because we have hemoglobin to bind O$_2$. When hemoglobin binds the oxygen, it upsets the balance and pulls more oxygen across the alveolar membrane. This is aided by pulmonary circulation which carries the blood away. Here's a demo of the diffusion process.