Why was hospitality so important to the ancient greeks and romans?

They value those people who traveled from afar and treats them with their cultural norm of reciprocity for being hospitable. They know the hardships of traveling at their time, especially walking and not having any water nor food.

Today people study hospitality like:

The hospitality and tourism industry has an inseparability of product and consumption. This means that the one cannot exist without the other. The tourism industry consumes the products that the hospitality industry creates. For example a tour bus full of tourists from overseas stops at a restaurant for lunch. A restaurant is considered part of the hospitality industry. Its function is to provide food and beverages to its clients. A tour bus full of tourists is considered part of the tourism industry. In conclusion the hospitality industry provides a product that the tourism industry consumes.