possibly it is a bug, you can try
1) restart the game
2) try the other doors in that scene
Hi I came across the same issue. Im not sure if it's intentional, but I was able to get through it.
After the cat initially runs away, I had to follow it at the fork by going right, continue to the left in the next area which then brought me back to the fork. After, I was unable to choose right at the fork and going left did nothing. I had to return to the woods entrance, talk to Lila, go back into the forest, which allowed me to choose the right path at the fork and in the next area it then spawned the cat to click. I was able to continue at this point.