When you generate the MOs from the AOs using LCAO, there are a number of rules that need to be followed.
-each MO has to conform to the symmetry of the system. With each symmetry element, the MO has to be either symmetric (symmetry operation leaves it the same) or antisymmetric (symmetry operation just changes all orbital signs)
- each MO has to be orthogonal to all other MOs. This means that the net overlap has to go to zero - this is probably what you mean by "cancellation"
at higher levels - each AO has to contribute "1" orbital overall, and each MO has to be equal to "1" orbital overall. At a qualitative level this isn't important.
Why symmetry and orthogonality? Mathematically, this is necessary for the equations to work. Physically, these will be the lowest energy orbitals.
For simple linear systems like you have here, the orbitals have increasing number of nodes as the energy increases. The lowest energy orbital always has zero, then 1, then 2, and so on until there is a node between each pair of atoms (for N atoms, N-1 nodes). These nodes have to be distributed symmetrically.