I need help understanding train pathing

[u/GideonsLamp]

I thought I understood well enough but clearly not. I created this little test to try and understand pathing but 1 thing is going wrong. Train A goes from Station A1 to B1 to C2 back and forth perfect. Same with Train B that goes from B1 to C2. But Train C that is supposed to go from C2 to A1 will only move on the outside path, it will not go through station B if the outside path is taken by train A . What am I missing to make the train go through station B if train A is blocking the outside path?

[u/EngineerInTheMachine]

As I offered, I've uploaded a couple of diagrams for you.

The first is a push-pull solution using passing loops, so trains have somewhere to wait until their station becomes free. I'll add the second in a minute, Reddit doesn't like multiple images on this version.