Genesis 16:12

And he shall be like the wild ass among men: his hands shall take vengeance of his adversaries, and the hands of his adversaries be put forth to do him evil; and in the presence of all his brethren shall he be commingled, (yitharbeb, Arabized,) and shall dwell.

‘PERE ADAM.’ Rashi comments: “One who loves the deserts is thus, according to Rashi, synonymous with “desert,” as it says peraim bamidbar (Job 24:5). Pere adam is thus: “a man who loves the desert.” (Mizrachi.) [and] to hunt wild animals, as it is written, And he dwelt in the wilderness and became an archer. His hand shall be against every man. This means that he will be a highway man. And every man’s hand against him. Everyone will hate him and attack him.”
The correct interpretation is that pere adam is a construct form, meaning that he will be a wild-ass man accustomed to the wilderness, going forth to his work, seeking for food, devouring all and being devoured by all. The subject pertains to his children who will increase, and they will have wars with all the nations.
Rabbi Abraham ibn Ezra said: “His hand shall be against every man in that he will be victorious at first over all nations, and afterwards, every man’s hand shall be against him, meaning that he will be vanquished in the end. And in the face of all his brethren, who are the sons of Keturah, he should dwell, meaning that Ishmael’s children will outnumber those of Keturah.”

פרא אדם. The word פרא describes a wild donkey, an animal that has not been domesticated. The angel told Hagar that the son she would bear would be genetically very similar in his character to a wild donkey. This would be due to his having part of the genes of his Egyptian mother. The prophet Ezekiel already described the Egyptians as being physically not much different from wild donkeys (Ezekiel 23,20) These characteristics would manifest themselves in the fact that he would make his home in the desert, a region not imposing restrictions on him. The Torah testifies to this in Genesis 21,20. The reason that the word אדם is added by the angel in describing Ishmael, was that he would inherit any human traits from his father Avram. The fact that he did possess such traits is confirmed by the Midrash which claims that he became a penitent before his father Avraham's death. (Baba Batra 16).

והוא יהיה; the letter ה at the beginning of the word והוא means that the angel's prophecy referred not only to Yishmael, but to his offspring as well. He foretold the characteristics of the Ishmaelites based on their founder's genes.

פרא אדם, a desert Bedouin, known as such because most Bedouins live in tents instead of in permanent dwellings. Compare Jeremiah 3,2 כערבי במדבר, "as an Arab, at home in the desert." [the word describes people who do not impose the restrictions upon themselves that civilized people accept in the interest of forming communities. Ed.] The Arabs are the people descended from the Ishmaelites.

ידו בכל, seeing that he will dwell in the desert, [a region in which there are no laws governing private property, Ed.] he will violate people's rights, and they in turn will outlaw him, putting a price on his head. In spite of living in constant friction with his neighbours he will not flee but will continue to dwell in their presence. When the angel concludes with the statement that he will ultimately die in the presence of כל אחיו, the word אחיו is used as a simile for the word שכניו, "his neighbours."