Why does NO₂ dimerise ?

Dimerisation is a process of association (addition reaction) of two similar molecules in order to gain stability which was absent in the monomer form.

NO₂ being unstable dimerises to N₂O₄ to exist as a stable molecule.

NO₂ beforehand, was an odd electron molecule (7+16=23) due to which it tries to unite with another of its kind to become stable.

That is why it dimerises.