Musar על בראשית 18:4

It is obvious to me that the מצוה of being hospitable to guests, (which is certainly included in the overall commandment to follow in G–d's footsteps), represents an additional virtue. The Torah has singled out this story of Abraham personally performing chores to entertain these strangers. It also alludes to the reward accruing to him, i.e. that everything he did personally for these guests, G–d later on personally did for Abraham's descendants, whereas whatever Abraham had designated to be done by someone else, G–d also performed for the Jewish people only by means of one of His agents. You should not think that all we talk about here is merely a part of a virtue. Whoever performs such an act such as Abraham's, performs the positive commandment of emulating G–d, and he will receive the reward due to someone who has performed a מצוה which has been specifically commanded. G–d performs acts of hospitality at all times, at every moment. Were He to desist from doing so for even a single moment the world would be lost. All creatures are His guests, we are all like strangers vis-a-vis G–d, and just as strangers we need a place to sleep. G–d enables us to survive. If He were to withdraw life-support for even a moment, we would all perish.

When Abraham told the three angels (men) at the time he invited them to come and rest under the tree, he already wanted to examine them as to their ritual purity. He did not say "rest under a tree," but "rest under THE tree." When Adam sinned, he sinned with the tree of knowledge. That tree brought death into the world. G–d Himself is on record as evicting Adam from the garden of Eden so that he should not be able to eat from the tree of life and thus live forever (Genesis 3,22).

I have already discussed why Abraham thought that if these guests had been human that they must have been sun-worshipers worshiping the dust of their feet. In order to remove that dust, he asked that they wash their feet by saying: יוקח נא מעט מים ורחצו רגליכם. We need to understand why he inserted the word מעט, a little, when he referred to the water they would wash their feet with. There is a deep significance in this.