Question

why was hospitality so important to the ancient greeks?

Answer 1

Travel in the ancient days was lengthy and often filled with hardships, and without hotels or places for travelers to stay hospitality became the only option. Maybe people who invited travelers into their homes feared punishment from the gods, rather than doing it from the good of their hearts. Fear of the wrath of the gods was prevalent in many Greek writings; for example, The Odyssey.
http://www1.union.edu/wareht/gkcultur/guide/8/web1.html