CRUD itself in OOP design

I just started learning web programming. When I design class diagram for Leave Online Management system. I I looked at this tutorial and started to get confused about my OOP knowledge.

I think, an object has only actions that it can do in the same way as it actually does. A Cow cannot milk itself. That must have 1 object like Farmer take milk from Cow or Farmer kill Cow(delete), change Cow(update). But my boss said that an object itself CRUD itself, it is OOP. The cow milked itself. I think Task cann't CRUD itself(exclude Create - Constructor). I think need a object like TaskManager for CRUD TASK. Where am I misunderstanding? Can anyone explain it to me? Thank you so much .!!!

P/s: Sorry for my English