I think my own belief in the Trinity is in harmony with the belief taught by my church. There is one God who simultaneously is a Father (Creator), Son (Jesus Christ), and Holy Spirit (this is God when he is communicating with us). It is like a man who simultaneously is a father, husband, brother, son, and banker … or whatever.
I don't think that would be a Trinitarian belief, because roles are not the same as Persons.
It would deny the ontological distinctions within the Godhead.
However, that is not to say your pastor is a non-Trinitarian. It could mean that he used an illustration that didn't reflect the reality. All of the different analogies fall short as they are based on the physical world. In addition, sometimes Trinitarian pastors don't use the best explanations, or people misunderstand them.
The best explanation I could give is that God is one in terms of essence (or being) and three in terms of Person, or personality. The Oneness describes the "what" and the Threeness describes the "who".
If I were to use human beings as an analogy, it would be like 3 different Persons occupying the same body (or essence). We don't have anything like that in creation, so it's hard to imagine. Even Siamese triplets have some degree of separation, but with God there is no separation.
Anti-Trinitarians will often say that doesn't make sense, but it is because they are viewing things according to their indoctrination and their assumption that everything about God must be reduced to their level for it to be true. They seem to refuse to consider that God's ontology could be something beyond their ability to understand.
All of us accept things that we cannot understand about God, though. For example, none of us understand how God existed since forever. We simply accept that this is true, without insisting that this truth must correspond with our experience.
The Trinity doctrine is pretty simple, and all five points are clearly taught in Scripture:
1. God is one.
2. The Father is God.
3. The Son is God.
4. The Holy Spirit is God.
5. The Father, Son, and Holy Spirit are three distinct Persons, each having a distinct Personality.
Each of the groups which deny the Trinity denies one or more of the above five points, yet all are taught clearly in Scripture.
Again, I'd recommend
James White's book
Forgotten Trinity in this regard.
As a young Christian, I was part of a defiant cult that claimed all others were unsaved, and one of the many reasons for their claim related to the Trinity, which they deemed to be a pagan doctrine. After coming to my senses a decade later, I realized that the Trinity doctrine is clearly taught in Scripture. The problem is that many are caught up listening to theological ignoramuses who project an air of authority, like my cult leader, Herbert Armstrong. It didn't help anything that my mother was a member of the same group.
The funny thing is that their own view of God's nature was pagan, as they were polytheists, believing in two separate god beings, God the Father and Jesus Christ. Polytheism, the belief in multiple gods, is clearly pagan. While hurling stones at Trinitarians for being pagans, they in fact were the ones holding pagan beliefs about God.
