When you are horizontal with an entity or player and relatively close, the pull function of the fishing rod works. However, when you start to get farther away from the player or entity, when fishing for them, they are not pulled towards you. This happens quite frequently when you are more than 15 blocks away and at an elevated height.
In the picture, the player isn't pulled where they are currently standing, but when they stand on the blue lapis block, it works sometimes but not always.
In the second picture, the player is horizontal with me, so they are able to be pulled.
In the last picture, the player is pulled 10% of the time.

I don't know if this is an intended feature, I however find this quite strange.