I'm going to get angry with my friend for buying a dog
I hope you're not serious, why would them getting a dog make you angry?
They are using the pet to cope with their depression
Depression is a legit reason to own a pet. You should be more supportive if your friend is depressed.
These are first world problems why can't people get over themselves?
Don't you think that's a viewpoint that's a little ignorant? Depression is a serious disorder with imbalances in brain chemicals, so someone can't just "get over it". Having an emotional support animal is wonderful since they are unconditionally loving, so why don't you try playing with the dog too?