It could have escaped from somebody. It also could be injured. As long as it is eating and drinking that is a good sign. I don't know much about birds but if it is used to humans, the more you keep feeding it the longer it will stay. Have you tried to touch it? Does it let you? If it does then it surely is domesticated. If you don't want to keep it you have to find some way to find it another home.

Its possible he had an encounter with a peregrine and is in a state of shock.But he should be ok in time.

Theres a tiny balcony at my daughters room.... 3 days ago i was shocked to see a pigeon in our balcony looking inside our window... first i ignored it thinking it would fly away but 3 hours later i noticed it was still there.. i thought to myself maybe its sick or something then i gave it water and a little rice... i was shocked it wasnt affraid of me but i didnt touch it.... the next morning i was amaize it was still there so i went to the grocery bought bird seeds.... gave it food again and water still didnt fly away.... its already 6 days its still there... im wondering if theres something wrong with it or if its ever going to fly away......