First, let's have some slightly more in-depth definitions. Charles Hodge describes what traducianists believe as follows:

Traducianists on the one hand deny that the soul is created; and on the other hand, they affirm that it is produced by the law of generation, being as truly derived from the parents as the body. The whole man, soul and body, is begotten. The whole man is derived from the substance of his progenitors.

Creationism, on the other hand, holds:

that the soul of the child is not generated or derived from the parents, but that it is created by the immediate agency of God.

Incidentally, and not surprisingly, both sides argue that Scripture is best understood to support their view. Among the Reformed, creationism is more widely held: Hodge and Louis Berkhof are among its proponents, while defenders of traducianism include William G. T. Shedd and A. H. Strong.

With that said, let's turn to the implications provided by the opponents of each view.

Traducianism

The issues include: (1) implied divisibility of the soul, (2) unorthodox tendencies of traducianists, and (3) a unity of substance between Adam and all mankind, and by extension, sinfulness of Christ's human nature.

(1) The first significant issue with traducianism, offered by both Berkhof and Hodge, is that it implies the divisibility of the soul. This, they say, contradicts the commonly held doctrine that the soul is a spiritual, immaterial substance. Hodge writes that "this is so serious a difficulty" that some proponents attempt to deny that division of the soul is implied in the theory, but Hodge sees only one other option, which is that all mankind is a single essence, and individual men are mere modes of existence—a doctrine Berkhof dismisses as "untenable."

Berkhof relates several other attempts to avoid this problem: (a) the child's soul pre-existed, (b) the soul is potentially present in the parents' sperm or egg or both, or (c) the soul is created in some way by the parents themselves. (A) implies pre-existence of the soul, (b) implies the materialism of the soul, and (c) implies creative power on the part of humans, and Berkhof accepts none of these.

Hodge, appreciative of the moderates who attempt to avoid these problems, writes:

If [traducianist] theologians and philosophers would content themselves with simply denying the creation of the soul ex nihilo, without insisting on the division of the substance of the soul or the identity of essence in all human beings, the evil would not be so great.

(2) Both Berkhof and Hodge express concern that many traducianists go further than necessary in the defense of their doctrine, and enter dangerous ground. Hodge first rebukes those who claim that the doctrine of original sin absolutely depends on traducianism:

We see theologians, ancient and modern, boldly asserting that if their doctrine of derivation [...] be not admitted, then original sin is impossible. That is, that nothing can be true, no matter how plainly taught in the word of God, which they cannot explain. [...] No man has a right to hang the millstone of his philosophy around the neck of the truth of God.

Berkhof and Hodge also warn that traducianists tend to assume that God now "operates only through means." That is, that God's creative work was finished in six days, and now he rests, and so the ongoing creation of souls is inconsistent with his relation to the world. But this, Hodge notes, sounds like deism, and imperils the doctrine of regeneration, which, Hodge says, "is due to the immediate exercise of the almighty power of God."

(3) Berkhof and Hodge note that traducianism normally implies the "theory of realism," which Hodge describes as follows:

Adam and his race are in such a sense one, that his act of disobedience was literally the act of all mankind. And consequently that they are as truly personally guilty on account of it, as Adam himself was; and that the inherent corruption flowing from that act, belongs to us in the same sense and in the same way, that it belonged to him.

This, they write, is problematic for several reasons. Berkhof notes that it implies the "untenable" position that all mankind is a single identical essence, and that it fails to give a satisfactory reason as to why men are held responsible only for Adam's first sin, and not all his subsequent sins. But, says Hodge, a greater issue exists: its implication on Christ's human nature.

Traducianists insist, Hodge says, that "Christ was in Adam as to the substance of his human nature as truly as we were," and that in order for him to be our redeemer, both his body and soul had to be "derived from the body and soul of his virgin mother." But this implies, says Hodge, that,

He must, therefore, be as much involved in the guilt and corruption of the apostasy as other men. [...] It is a contradiction to say that we are guilty of Adam's sin because we are partakers of his essence, and that Christ is not guilty of his sin nor involved in its pollution, although He is a partaker of his essence.

Hodge concludes:

As this seems a legitimate conclusion from the traducian doctrine, and as this conclusion is anti-Christian, and false, the doctrine itself cannot be true.

Creationism

Strong and Shedd raise these issues with creationism: (1) human reproduction becomes inferior to animal reproduction, (2) its difficulty in explaining original sin, and (3) it implies that God is the author of evil.

(1) Under creationism, earthly parents beget only the body of their child. This implies that beasts "possess nobler powers of propagation than man; for the beast multiples himself after his own image." (Strong) It also fails to take into account the similarities between children and their parents.

(2) Shedd argues that creationism has difficulty when it comes to explaining original sin:

Sin cannot be propagated, unless that physical substance in which sin inheres is also propagated. Sin cannot be transmitted along absolute non-entity. Neither can it be transmitted by a merely physical substance. If each individual soul never had any other than an individual existence, and were created ex nihilo in every instance, nothing mental could pass from Adam to his posterity.

Shedd remarks that "the creationist partially adopts traducianism" in order to explain the transmission of sin with other theories, like the theory of representative union.

(3) Shedd then turns to the universality of sin, and argues that creationists cannot adequately explain it. In creationism, he says, "the fall is that of the individual only. Each soul apostatizes from God by itself."

One possible response, that God withdraws grace at the instant in which he creates the new soul, is inconsistent with God's dealing with Adam, says Shedd: God withdrew grace from Adam only after Adam's sin, not before, but here, the "withdrawing of grace occurs not because of apostasy, but in order to produce it."

A second response, says Shedd, is that the withdrawal of grace is due to Adam's transgression. This being closer to the traducianist position, Shedd finds it more agreeable, but finds fault with its failure to recognize a unity of substance:

From the creationist position, a newly created and innocent soul that never was substantially one with Adam, and did not participate with him in the first transgression, is deprived of certain created gifts by an act of sovereignty. There is no reason, upon this theory, why by the same sovereignty men might not be deprived of Divine gifts on account of the transgression of Lucifer. Upon the theory of creationism, the withdrawal of the Holy Spirit from the newly created soul is an arbitrary, not a judicial act.

The new soul's guilt, Shedd says, is the "product of an act of sovereign will which decides that an innocent person shall be liable to penal suffering because of another's sin." This, Shedd says, destroys all ethics and dangerously implicates God with unrighteousness:

As in the gospel scheme there is a "righteousness of God," that is, a constructive and unmerited righteousness, when the obedience of Christ is gratuitously imputed, so in this scheme there is an "unrighteousness of God," that is, a constructive and unmerited unrighteousness, when the disobedience of Adam is gratuitously imputed.

To those creationists who attempt to respond to this problem by splitting punishment from culpability and saying that Adam's posterity are punishable for his sin, but not culpable for it, Shedd argues that the two are as inseparable as cause and effect, that punishing one who is not guilty is inherently unjust, and that such separation attempts serve to introduce semi-Pelagianism and Arminianism into the Reformed tradition.

Berkhof admits that this is "[t]he most serious objection" to creationism, as Strong summarizes:

[Creationism], if it allows that the soul is originally possessed of depraved tendencies, makes God the direct author of moral evil; if it holds the soul to have been created pure, it makes God indirectly the author of moral evil, by teaching that He put this pure soul into a body which will inevitably corrupt it.

Monism

John Frame rejects both views on the basis of his position that the body and soul are not distinct metaphysical components of the human person:

[T]he soul is not a separable part of a person. It is rather the person himself, seen from a particular aspect. So there is no particular period in time when the body exists without a soul, nor any point in time when a soul is added to a soulless body. The soul exists from conception, for it is an aspect of the total person, who exists from conception.

This view, a form of monism, is not directly addressed by any of the previously quoted authors, though all of them argue that body and soul are distinct. For example, Berkhof writes:

In Gen. 2:7 a clear distinction is made between the origin of the body and that of the soul. [...] In these simple words the twofold nature of man is clearly asserted, and their teaching is corroborated by other passages of Scripture.

Conclusion

Berkhof concludes his analysis of these views with the following cautionary remarks:

It must be admitted that the arguments on both sides are rather well balanced. In view of this fact it is not surprising that Augustine found it rather hard to choose between the two. [...] And because we have no clear teaching of Scripture on the point in question, it is necessary to speak with caution on the subject.

References

• Berkhof, Systematic Theology, 2.1.1.B.4 and 2.1.2 (p. 183, 195, 197-201)
• Frame, Systematic Theology, 801-2
• Hodge, Systematic Theology, Volume II, chapter 3 and chapter 5
• Shedd, Dogmatic Theology, Volume II, 29-53
• Strong, Systematic Theology, Volume II, 491-93