The anti-bonding molecular orbitals are higher in energy than the constituent atoms in a diatomic molecule. That means it is less stable. Why does it form? Why can't all the molecular orbitals be bonding molecular orbitals?
Molecular orbitals form when you apply the "Linear Combination of atomic orbitals" (LCAO) model to atoms bonding. Where you take a linear combination of the relevant atomic orbitals to create an MO. In each case of combination a bonding and an anti bonding (ab) combination forms. The ab MO form as a result of applying the Huckel model which results in a square root in the expression for the energy, thus giving a negative and a positive contribution to the energy. One of the expressions E1 will be lower in energy and will form the bonding and the second E2 will form the higher energy MO - anti bonding. Sometimes a non-bonding orbital forms, which doesn't contribute to the total bond energy, where the squared root expression equals zero.
To understand it more thoroughly one needs to understand the hydrogen atom quantum model and it's solution which give the orbitals we know as: s,p,d,f etc. In the case of MO we apply say that each atom "brings" it's set of occupied orbitals from it's valence electronic shell, combining these gives MO diagrams. It's an approximation but the results it gives describe to some extent what can be measured in the lab.