Adam Clarke on Numbers 20:21

Thus Edom refused to give Israel passage through his border - Though every king has a right to refuse passage through his territories to any strangers; yet in a case like this, and in a time also in which emigrations were frequent and universally allowed, it was both cruelty and oppression in Edom to refuse a passage to a comparatively unarmed and inoffensive multitude, who were all their own near kinsmen. It appears however that it was only the Edomites of Kadesh that were thus unfriendly and cruel; for from Deu 2:29 we learn that the Edomites who dwelt in Mount Seir treated them in a hospitable manner. This cruelty in the Edomites of Kadesh is strongly reprehended, and threatened by the Prophet Obadiah, Oba 1:10, etc.