(1) God is love.
(2) In order for love to obtain, there must exist love and a lover as well as an object of love (a beloved).
(3) Therefore, God must be tripersonal with the Father as lover (subject), the Son as beloved (object) and the Holy Spirit as the bond of love obtaining between Father and Son.
However, German theologian Wolfhart Pannenberg (who is also a Trinitarian) rejoins:
Any derivation of the plurality of trinitarian persons from the essence of the one God, whether it be viewed as spirit or love, leads into the problems of either modalism on the one hand [i.e., as in the case of Karl Barth] or subordinationism on the other. Neither, then, can be true to the intentions of the trinitarian dogma. The derivation from love is closer to the Christian concept of God and the doctrine of the Trinity than is derivation from the idea of divine self-consciousness, since it leaves more room for a plurality of persons in the unity of the divine life. Yet this plurality cannot be deduced from an idea of love without relapse into a pretrinitarian monotheism, that of the subjectivity of the one God as the one who generates the other persons. In the concept of divine love it can find only their comprehensive unity (Systematic Theology, 1:298).
Pannenberg would rather believe that God as a whole is love (1 John 4:8)--Almighty God does not simply love or have love in his estimation. This approach eradicates any notions (Pannenberg argues) of one divine subject loving a divine object or one divine person being the love that obtains between the Father and the Son. It seems Pannenberg wants to argue that the whole Godhead is love; hence, he appears to take exception to the line of argumentation employed by Augustine of Hippo or Richard of Saint Victor. Moreover, he appears to mention the Father generating the other divine persons in a less than commendatory way.
But the Father is the referent of ὁ θεὸς in 1 John 4:8: let's not forget that point. For example, 1 John 4:9 reads: "This is how God showed his love among us: He sent his one and only Son into the world that we might live through him" (NIV). The "God" (ὁ Θεὸς) mentioned in that verse who sent his Son is the Father, not the Son or the Holy Spirit. Therefore, the whole argument from love approach is ill-fated for yet another reason.
For a sound Trinitarian critique of the eternal generation idea, see John Feinberg's work No One Like Him.