I don’t think it’s possible to give you a satisfactory answer, MH84.
The inner nature of God is not something that human reason can comprehend. What little we do know about the Trinity has been revealed to us by God, not worked out by us on our own.
It’s true that the Scriptures are not as specific about the Trinity as some later theological statements have been. On the other hand, as Catholics we believe that the Scriptures, while inspired of God, are not the totality of Revelation.
Catholic teaching is based on what Jesus taught the apostles, and what the Holy Spirit led the apostles to teach, a great deal of which is recorded or at least alluded to in the Scriptures.
Later philosophical definitions were arrived at because they seemed to best explain and defend the truth as it had been revealed. The early Christians, being Jewish in background, knew there was only one God. Yet Scripture sometimes describes Jesus as possessing traits proper only to God, and seems to present Jesus and His Father as distinct entities in some sense. Likewise, the Holy Spirit sometimes seems to be a name for the power or activity of God, but at other times Jesus talks of the Spirit as a personal entity, distinct from both Himself and the Father. And it’s possible to blaspheme against the Holy Spirit, a sin Jesus considered more terrible than blasphemy against Himself. Finally, the apostled handed down from Jesus Himself the teaching that baptism should be performed “in the name of the Father and of the Son and of the Holy Spirit,” seemingly putting the three on the same level.
So, out of the revealed Tradition (including the written Scripture), we have three entities that are distinct enough to have different names or titles, all of whom are described at one time or another as possessing the traits of God. Yet we have only one God, and must worship Him alone.
It’s only natural that Christians would debate exactly what was being revealed to them in these teachings. That especially happened when someone would publicly put forward an interpretation that seemed a little “off” to other people, as though it maybe overemphasized one aspect of the revelation and didn’t grapple properly with the others. Eventually, over the course of multiple Councils, the bishops hammered out very precise philosophical statements about the relationships within the Trinity. Naturally, these were more detailed than the Scriptural data, because the exact problem was the many interpretations one could put on that data. The bishops wanted a clear statement that they could point to and say “This is what Jesus and the apostles meant, expressed as exactly as we can manage it. If you teach something else, you have gotten it wrong somewhere down the line.”
Attempts at explaining the Trinity by analogy, such as the lover/beloved/love idea, can be helpful, but are necessarily limited and should not be taken as central to the teaching itself.
So … why are there three Persons in the Godhead, no fewer and no more? If you are asking that in an absolute sense, there is no answer. There’s no “why” to God; He is the way He is. If you are asking why the Church recognizes three Persons and not some other number, it is because that is what the data of revelation suggest. We are told of Father, Son, and Spirit, but no others like them.
Why, in the “lover/beloved/love” analogy, does the love between Father and Son manifest as one Person rather than two? Well, because the analogy is just that – a way of trying to make sense of what we are already told, namely that God is one yet three. Since four is not given as an option, the analogy does not attempt to go there.
Why is it taught that each Person possesses the Divine Nature in full rather than dividing it up? That’s just a matter of reasoning from premises to conclusions. In this case, since God is held to be infinitely simple and without parts, it is simply not possible that the Persons “split” the Nature. Likewise, the language of revelation indicates that each Person is God in His own right, not one of a set of sub-gods that snap together to make the full God like some Transformers toys.
Why do we teach that the Holy Spirit is God right alongside the Father and Son? Well, obviously that’s not as clear in the data of revelation, since it took a bit longer for the Spirit’s status to be definitively settled than it did for the other two. However, as I noted above, even in Scripture itself we see the Spirit referred to as a personal entity (not just a power or force) with attributes proper only to God. And of course, the baptismal formula (which soon became the universal Christian blessing) seems to place all three on the same level and declares that they have between them only a single name.
Does that help at all?
Usagi