Tamed cats and wolves will not teleport to the player if its path is blocked by fences or vertically-oriented trapdoors, and sometimes if its path is blocked by solid blocks.  It happens when an animal is "trapped" (by fences and/or vertical trapdoors, like found in some villages) (this happens 100% of the time and is repeatable), or when an animal is inside a building and can't get out (happens about 50% of the time).

(Villagers also have trouble navigating out of the trapdoor garden boxes.)

Steps to recreate:

Place four trapdoors around an empty space and open them (making them orient vertically), creating a one block "pen".  Put a tamed cat or wolf inside and walk away.  It will not follow you or teleport to you.  If you close one of the trapdoors, opening the pen, then it will follow you and be able to teleport to you.

Alternate: put a closed loop of fences around a tamed cat or wolf.  Walk far enough away that it should teleport to you, but it will not.