Commentaire sur Les Nombres 20:18

פן בחרב אצא לקראתך LEST I COME OUT AGAINST THEE WITH THE SWORD — You pride yourselves on the “voice” which your father bequeathed you as a blessing, saying, “And we cried unto the Lord and He heard our voice” (cf. Rashi on v. 16); I, therefore, will come out against you with that which my father bequeathed me when he said, (Genesis 27:40) “And by thy sword shalt thou live” (Midrash Tanchuma, Beshalach 9 on בשלח)

פן בחרב אצא לקראתך, most of the people of Edom were bloodthirsty people and did not need more than the slightest pretext in order to start a war.

ויאמר אליו אדום, “Edom said to him, etc.” The Torah no longer adds the title “king” when speaking of Edom, indicating that the whole nation concurred with their King’s refusal to allow the Israelites passage through their country.