In the video you posted, the animals don't eat the crops but the undergrowth in front of them. You should try growing hay, because animals will eat that right off the field and it does not take as long to grow.
Why the animals never finish their eating assignment, I can't say. It might be best to search your mods.
Mods that change the tasks queues or something like that might also influence your animals, even if they are only intended for humans.
Most of the time you can find on the mod page in the forum/on the steam mod page the known issues the mod can cause.
It could probably be that Scarecrow Mod, if the mod is supposed to prevent wild animals from damaging your fields.
I don't use the mod myself, but watching the video for the second time I noticed the scarecrow.