I am a brother to dragons - That is, my loud complaints and cries resemble the doleful screams of wild animals, or of the most frightful monsters. The word "brother" is often used in this sense, to denote similarity in any respect. The word "dragons" here (תנין tannı̂yn), denotes properly a sea-monster, a great fish, a crocodile; or the fancied animal with wings called a dragon; see the notes at Isaiah 13:22. Gesenius, Umbreit, and Noyes, render this word here jackals - an animal between a dog and a fox, or a wolf and a fox; an animal that abounds in deserts and solitudes, and that makes a doleful cry in the night. So the Syriac renders it an animal resembling a dog; a wild dog. Castell. This idea agrees with the scope of the passage better than the common reference to a sea-monster or a crocodile. "The Deeb, or Jackal," says Shaw, "is of a darker color than the fox, and about the same bigness. It yelps every night about the gardens and villages, feeding upon roots, fruit, and carrion." Travels, p. 247, Ed. Oxford, 1738. That some wild animal, distinguished for a mournful noise, or howl, is meant, is evident; and the passage better agrees with the description of a jackal than the hissing of a serpent or the noise of the crocodile. Bochart supposes that the allusion is to dragons, because they erect their heads, and their jaws are drawn open, and they seem to be complaining against God on account of their humble and miserable condition. Taylor (Concord.) supposes it means jackals or thoes, and refers to the following places where the word may be so used; Psalm 44:19; Isaiah 13:22; Isaiah 34:13; Isaiah 35:7; Isaiah 43:20; Jeremiah 11:11; Jeremiah 10:22; Jeremiah 49:33; Jeremiah 51:37; Lamentations 4:3; Micah 1:8; Malachi 1:3.
And a companion to owls - Margin, ostriches. The word companion here is used in a sense similar to brother in the other member of the parallelism, to denote resemblance. The Hebrew, here rendered owls, is, literally, daughters of answering, or clamor - יענה בנות benôth ya‛ănâh. The name is given on account of the plaintive and mournful cry which is made. Bochart. Gesenius supposes, however, that it is on account of its greediness and gluttony. The name "daughters of the ostrich." denotes properly the female ostrich. The phrase is, however, put for the ostrich of both sexes in many places; see Gesenius on the word יענה ya‛ănâh; compare the notes at Isaiah 13:21. For a full examination of the meaning of the phrase, see Bochart, Hieroz. P. ii. L. 2. cap. xiv. pp. 218-231; see also Job 39:13-17. There can be little doubt that the ostrich is here intended, and Job means to say that his mourning resembled the doleful noise made by the ostrich in the lonely desert. Shaw, in his Travels, says that during the night "they (the ostriches) make very doleful and hideous noises; which would sometimes be like the roaring of a lion; at other times it would bear a nearer resemblance to the hoarser voice of other quadrupeds, particularly of the bull and the ox. I have often heard them groan as if they were in the greatest agonies."

I am a brother to dragons - By my mournful and continual cry I resemble תנים tannim, the jackals or hyenas.
And a companion to owls - בנות יענה benoth yaanah, to the daughters of howling: generally understood to be the ostrich; for both the jackal and the female ostrich are remarkable for their mournful cry, and for their attachment to desolate places - Dodd.

I am a brother to (u) dragons, and a companion to owls.
(u) I am like the wild beasts that desire solitary places.

I am a brother to dragons, and a companion to owls. Or ostriches, as the Targum, Septuagint, Vulgate Latin, Syriac, and Arabic versions; either he was obliged to dwell with such persons as were comparable to these creatures for their devouring words, hissing noise, and venomous speeches, or for want of compassion, and for their cruelty, as David is said to be among lions, Psalm 57:4; or also, he was like unto them, being solitary and alone, all his friends and acquaintance standing at a distance from him, as these creatures love lonesome and desolate places; or because of the wailing and howling noise they make, to which his mournful notes bore some resemblance; see Gill on Micah 1:8; or because, when these creatures cry and howl, and make a noise, no mercy is shown to them, none pities or regards them; and so it was with him; though he stood and cried in ever so public a manner, none had any compassion on him.

dragons . . . owls--rather, "jackals," "ostriches," both of which utter dismal screams (Micah 1:8); in which respect, as also in their living amidst solitudes (the emblem of desolation), Job is their brother and companion; that is, resembles them. "Dragon," Hebrew, tannim, usually means the crocodile; so perhaps here, its open jaws lifted towards heaven, and its noise making it seem as if it mourned over its fate [BOCHART].

A brother - By imitation of their cries: persons of like qualities are often called brethren. Dragon - Which howl and wail mournfully in the deserts.