When tethering mobs in the latest version of the game, the leads are stretched too much compared to later versions, which makes mobs untie more easily in some cases and also makes them approach you more slowly when you lead them with the leads.
The first video is of the later version and the second is of a latest version
I have experienced this as well. It is now nearly impossible to lead mobs by hand over any terrain that is not completely flat. The mob will not follow and the lead eventually breaks.