When two atomic orbitals make one molecular orbital there must be an antibonding orbital also. Why should they make also an antibonding molecular orbital, such as the $2\mathrm b_2$ orbital in the scheme below?
Why should they make also an antibonding molecular orbital?
Orbital symmetry must be conserved. Thus, when you mix orbitals, the number of orbitals must also be conserved. As a consequence, when two orbitals are operated on to produce new orbitals, two new orbitals must be created.
Think about it conceptually this way: When two orbitals that have the same symmetry and appropriately matched energy come together, a bonding orbital is formed. This bonding orbital contains all of the "good orbital stuff" from that pair of orbitals. But, because there were two orbitals originally, there has to be "orbital stuff" left over. This leftover "orbital stuff" forms the antibonding orbital.
Now, the screwy part is that orbitals are not real. They are mathematical constructs to describe the wave-like probabilistic properties of electrons. If there are no electrons in the orbital, then the orbital is not really "there". So, while an antibonding orbital is formed, it is not real unless it has electrons in it. In the case of water above, the antibonding orbitals are not populated, so they don't exist.