What would be the appropriate answer to a non-Muslim asking about the reason for growing a beard?

Shaving the beard is obligatory. If a non-Muslim asks you for the reason, explain to him that it is an act of obedience to Allah and His Messenger, and that it is from the Sunan of Fitra (natural disposition) upon which Allah created the monotheists, and from the guidance of the Prophets. This is similar to what Salman al-Farisi (may Allah be pleased with him) did when the polytheists mockingly asked him about the Prophet's (peace be upon him) teaching them everything, even relieving themselves. Salman answered them by explaining the rulings and etiquette of istinja (definition)' (cleaning oneself after relieving oneself).