The interaction vertices don't allow for a u-channel diagram where the final state nucleon and antinucleon cross. You can check this by trying to draw such a diagram by starting with the initial and final state lines and then trying to insert vertices to connect them. If you consider the nucleon-nucleon interaction, you would find t and u-channel diagrams, but no s-channel.
I think I see why there is no s channel in the nucleon nucleon case. Is this because, if there were an s channel diagram, we would have 2 [itex]\psi[/itex] particles on the left of the 1st vertex and 0 [itex]\psi[/itex] particles on the right? Since the number of psi particles is a quantum number, it must be conserved and so this diagram is unphysical.
I tried applying a similar argument to the u channel diagram in the nucleon-antinucleon case but I just cannot see why it won't work! Can you elaborate please?