Why didn't Moshe eat or drink for 40 days when he went to Shomayim? The Medrash says "עלת לקרתא הלך בנימוסיה" or as we say "when in Rome do as the Romans do"!!!
Lesson in Derech Eretz: Fit in. Respect your hosts. Follow their cues.
In the same vein: Why do we say שלום עליכם בואכם לשלום ברכוני לשלום and welcome the angels so warmly on Friday night. Then we abruptly say צאתכם לשלום - BYE BYE NOW!!! They just got here and we are already sending them away?
Answer - We are about to eat. They can't eat. It is impolite to eat in their presence. So we politely send them off.