Opposite linkage is a special Portal 2 coop mode, where Atlas' primary portal is connected to P-body's secondary portal and P-body's primary portal is connected to Atlas' secondary portal. So players instead of controlling separate sets of portals, they both control half of the mutual sets.
I'm aware of the glitched portal rendering on second player side, but I have no idea how to fix this. This is however only graphical glitch, which really have minimal impact on the gameplay.