It has been noted that for every degeneracy along a reaction coordinate there is a molecular orbital crossing. Thus for the butadiene to cyclobutene conversion, the two Möbius (here conrotatory) and Hückel (here disrotatory) modes are shown in Figure 5. The starting MOs are depicted in the center of the correlation diagram with blue correlation lines connecting MOs. It is seen that for the Möbius mode the four electrons in MOs 1 and 2 end in the bonding MOs (i.e. σ and π) of cyclobutene. In contrast, for the Hückel mode, there is a degeneracy and thus an MO crossing leading to two electrons (drawn in red) are headed for an antibonding MO. Thus the Hückel mode is forbidden while the Möbius mode is allowed. 
One further relevant point is that the first organic correlation diagrams were in a 1961 publication on carbanion rearrangements. It had been noted that when an occupied molecular orbital becomes antibonding the reaction is inhibited and this phenomenon was correlated with a series of rearrangements.