Christ’s flesh was identical to our own

…what is blood but red fluid? what is flesh but earth in an especial form? Consider the respective qualities,—of the muscles as clods; of the bones as stones; the mammillary glands as a kind of pebbles. Look upon the close junctions of the nerves as propagations of roots, and the branching courses of the veins as winding rivulets, and the down (which covers us) as moss, and the hair as grass, and the very treasures of marrow within our bones as ores of flesh. All these marks of the earthy origin were in Christ; and it is they which obscured Him as the Son of God, for He was looked on as man, for no other reason whatever than because He existed in the corporeal substance of a man.

Tertullian
On the Flesh of Christ
Chapter IX

Heretics use the Scriptures to try and deny that God was actually born of a woman

But whenever a dispute arises about the nativity, all who reject it as creating a presumption in favour of the reality of Christ’s flesh, wilfully deny that God Himself was born, on the ground that He asked, “Who is my mother, and who are my brethren?”

Tertullian
On the Flesh of Christ
Chapter VII

Christ birth and death are linked. You can’t have one without the other.

When, therefore, they set forth the flesh of Christ after the pattern of the angels, declaring it to be not born, and yet flesh for all that, I should wish them to compare the causes, both in Christ’s case and that of the angels, wherefore they came in the flesh. Never did any angel descend for the purpose of being crucified, of tasting death, and of rising again from the dead. Now, since there never was such a reason for angels becoming embodied, you have the cause why they assumed flesh without undergoing birth. They had not come to die, therefore they also (came not) to be born.

…The law which makes us die is the cause of our being born. Now, since Christ died owing to the condition which undergoes death, but that undergoes death which is also born, the consequence was—nay, it was an antecedent necessity—that He must have been born also, by reason of the condition which undergoes birth; because He had to die in obedience to that very condition which, because it begins with birth, ends in death.

Tertullian
On the Flesh of Christ
Chapter VI

The nature of the hypostatic union — God and man

Christ could not be described as being man without flesh, nor the Son of man without any human parent; just as He is not God without the Spirit of God, nor the Son of God without having God for His father. Thus the nature of the two substances displayed Him as man and God,—in one respect born, in the other unborn; in one respect fleshly, in the other spiritual; in one sense weak, in the other exceeding strong; in one sense dying, in the other living. This property of the two states—the divine and the human—is distinctly asserted with equal truth of both natures alike, with the same belief both in respect of the Spirit and of the flesh. The powers of the Spirit, proved Him to be God, His sufferings attested the flesh of man.

Tertullian
On the Flesh of Christ
Chapter V

The Incarnation is foolishness to man

But, Marcion, consider well this Scripture, if indeed you have not erased it: “God hath chosen the foolish things of the world, to confound the wise.” Now what are those foolish things? Are they the conversion of men to the worship of the true God, the rejection of error, the whole training in righteousness, chastity, mercy, patience, and innocence?  These things certainly are not “foolish.” Inquire again, then, of what things he spoke, and when you imagine that you have discovered what they are will you find anything to be so “foolish” as believing in a God that has been born, and that of a virgin, and of a fleshly nature too, who wallowed in all the before-mentioned humiliations of nature?  But some one may say, “These are not the foolish things; they must be other things which God has chosen to confound the wisdom of the world.” And yet, according to the world’s wisdom, it is more easy to believe that Jupiter became a bull or a swan, if we listen to Marcion, than that Christ really became a man.

Tertullian
On the Flesh of Christ
Chapter IV

If angels could become men in the scriptures and remain angels, then why couldn’t Christ become man and remain God?

You have sometimes read and believed that the Creator’s angels have been changed into human form, and have even borne about so veritable a body, that Abraham even washed their feet, and Lot was rescued from the Sodomites by their hands; an angel, moreover, wrestled with a man so strenuously with his body, that the latter desired to be let loose, so tightly was he held. Has it, then, been permitted to angels, which are inferior to God, after they have been changed into human bodily form, nevertheless to remain angels? and will you deprive God, their superior, of this faculty, as if Christ could not continue to be God, after His real assumption of the nature of man? Or else, did those angels appear as phantoms of flesh? You will not, however, have the courage to say this; for if it be so held in your belief, that the Creator’s angels are in the same condition as Christ, then Christ will belong to the same God as those angels do, who are like Christ in their condition. If you had not purposely rejected in some instances, and corrupted in others, the Scriptures which are opposed to your opinion…

 

Tertullian 
On the Flesh of Christ
Chapter III

Christ did not cease to be God when he became man

Why, I want to know, was it of so much importance, that Christ should, when perfectly aware what He really was, exhibit Himself as being that which He was not? You cannot express any apprehension that, if He had been born and truly clothed Himself with man’s nature, He would have ceased to be God, losing what He was, while becoming what He was not. For God is in no danger of losing His own state and condition.

Tertullian 
On the Flesh of Christ
Chapter III

God willed to be born in the likeness of man

Since you think that this lay within the competency of your own arbitrary choice, you must needs have supposed that being born was either impossible for God, or unbecoming to Him. With God, however, nothing is impossible but what He does not will. Let us consider, then, whether He willed to be born (for if He had the will, He also had the power, and was born). I put the argument very briefly. If God had willed not to be born, it matters not why, He would not have presented Himself in the likeness of man.

Tertullian
On the Flesh of Christ
Chapter III

The incarnation of God is the weakness of God though stronger than men

Now, what is that “foolishness of God which is wiser than men,” but the cross and death of Christ? What is that “weakness of God which is stronger than men,” but the nativity and incarnation of God?

Tertullian
The Five Books Against Marcion, Book V
Chapter V