I summarized White’s 6 reasons into 3 top reasons:
1: Unity and Equality of Divine Persons (Monotheism)
The doctrine of the divine nature, which tells us what God is, allows us to properly explain how each of the three persons are truly the one God. As such, this doctrine helps to qualify important analogies, like the psychological analogy, to ensure that the Father, Son and Holy Spirit are equal.
2: Real Distinction of Divine Persons (Trinitarian)
The doctrine of the divine nature also allows us to state that the Father, Son and Holy Spirit are each the one God (entirely equal in essence & one in being) and thereby affirm that we can distinguish the persons by relations of origin (this was the common way among Greek and Latin traditions of the Church) that are substantial rather than accidental (this was St. Augustine’s insight). The Father, Son and Holy Spirit are truly relative to one another in all they are, as subsisting relations.
Therefore, the Father, Son and Holy Spirit can be present to one another personally (i.e. perichoresis) because they each possess the plenitude of divine life.
3: Essential to distinguish eternal processions from temporal missions (Trinitarian Monotheism)
The doctrine of the divine nature helps us to uphold both (1) the transcendence of the Trinity, as the one God and Creator, utterly distinct from creatures in his incomprehensible mystery; (2) the omnipresence and immanence of the Trinity to all of creation; (3) the unique ways the eternal processions in the godhead are manifest in their temporal missions.
“This is nowhere truer than in the case of the visible mission of the Word, in which he takes on a human nature in the Incarnation. In virtue of the hypostatic union, the second person of the Trinity subsists in two natures, without confusion or separation. In virtue of one of these natures, which is mysterious and incomprehensible, he is one with the Father and the Spirit. He is true God and Lord. In virtue of the other he is truly human, and possesses a humanity mysteriously perfected by a plenitude of grace. Christ’s hypostatic person, which subsists in both divine and human natures, is the locus par excellence of the revelation of the Trinity. We cannot approach this mystery rightly, however, in its almost unfathomable depths, if we do not also acknowledge a theology of the divine nature of Christ, the nature in virtue of which he is truly one with the Father and the Spirit, and in which he is naturally distinct from us, insofar as, unlike all other human beings, he is truly God” (678).
Prodigal Catholic 