An intuitive way of looking at this is that when you have many atoms to consider, there will be multiple bonding/antibonding interactions between atoms. Whether the MO is overall bonding or antibonding will depend on the sum of these interactions. This is rather simplified, but using the example of benzene again, we can examine the three bonding π MOs:
MO 1 (the lowest-energy π MO) has one nodal plane in the plane of the ring. However, because this isn't a plane separating two constituent atomic orbitals (the p orbitals), this nodal plane doesn't tell us anything about bonding/antibonding properties of the MO. Indeed, this nodal plane only arises because the building blocks – the p-orbitals – have a node in their centre. The interactions between different p-orbitals are all bonding in nature, because the shaded (positive) lobes of each p-orbital are overlapping with the shaded lobes of their neighbours (and vice versa for the unshaded lobes).
MO 2 has a nodal plane between p-orbitals, which suggests the presence of antibonding character. That is true: there are two major antibonding interactions, one between the top-left and top-right carbons, and one between the bottom-left and bottom-right carbons. (The middle-left and middle-right carbons are too far apart). However, there are also multiple bonding interactions: the three carbons on the left, for example, are all interacting with each other in a bonding fashion. Overall, this MO is bonding, although not quite "as bonding" as MO 1.
Likewise, MO 3 has antibonding interactions between the top-left and bottom-left carbons (for example). It also has bonding interactions between the top-left and top-right carbons. However, the antibonding interactions are occurring over a greater distance than the bonding interactions. Consequently, they are weaker than the bonding interactions, and again we have a case of net bonding.