Dad saying he'll get rid of my dog

My dad is constantly threatening to put my dog (2 years old, we got him at 2 months old) up for adoption. I love my dog more than anything in this world and would probably fall into a deep depression if he actually did it (on top of my other various mental issues). He threatens this when I can't take care of him-- for example, today, I was in the middle of making my bed and my dog was barking at him (and had been for a while), so he told me to take care of him. I told him I would in a minute but couldn't right then because I was in the middle of something, and he screamed at me that he's going to put him up for adoption. Another example is that if I'm exhausted and can't walk the dog, he threatens this.

I know my dad loves him too and had wanted a dog all his life before we got him. I'm really hoping it's just a threat and he's only saying it to scare me.

Is this normal behavior? Should I drop everything to take care of the dog? Should I be forced to walk him when I'm exhausted? How do I do that without feeling terrible?