He's basically arguing here that the orthodox concept of "person" is inherently modalistic, which is insane; it would leave the Trinity as an incoherent antinomy between modalism and tri-theism. But the reason they can't get their heads around the concept of "person" (which is what this would require) is that they can't conceive of "person" except in anthropomorphic terms, even though equating divine personhood with human personhood generates an absurd tri-theism.
Because Prejean just isn’t up to the task of answering the real arguments, he is now taking refuge in straw man arguments.
No one is equating divine personhood with human personhood. A person of the Godhead differs in fundamental respects from a human person, just as a theanthropic consciousness is not the same as a merely human or merely divine mind.
On the one hand, revelation assigns personal traits to divine subjects (Christ, the Trinity)—traits we designate as personal precisely because they are analogous with human experience.
On the other hand, revelation also assigns to divine subjects certain attributes which are disanalogous with human experience, viz. omnipotence, omniscience, eternality, triunity.
In framing our doctrine of God and Christ, we make full allowance for the revealed discontinuities as well as the revealed continuities.
The same interpretive methods disclose both the analogous and disanalogous attributions. No arbitrary gear-shifting to the silly putty exegesis of the allegorical method is required.
All this is quite different from Prejean’s merely made-up distinctions and fictitious definitions—superimposed upon the inkblot of a selective and opportunistic allegorism.