Why is air a form of matter?
Because it is. Has mass, has density, reacts, is made of protons/neutrons/electrons
If i take matter like water, then it has a freezing point and boiling point. At -20C, it is solid ice. At 20C it is liquid water. At 120C it is gas.
If i take the oxygen in the air, it is exactly the same above - the only difference is that the temperatures are different.
Oxygen melts at -218C and boils at -183C. If you have oxygen at -250C, it is solid just like ice (or close enough). If you have it at -200C, it is a blue-ish liquid. If you have it at -100C, it is a gas.
At room temperature it is a gas (or a significant component of air). The same can be said for the nitrogen in air, but just at different temperatures.