The doctrine of the Trinity seems to be a constant speed bump between LDS and Evangelicals. For one, it’s a difficult doctrine to comprehend. One thing that helps me understand the necessity of the doctrine of the Trinity is this:
Any attribute that we give to God must not be contingent on anything else. God (by classical Christian understanding) cannot rely on something or someone else for definition or power. No one gives God power or characteristic except for God alone. He exist absolutely and completely whether anyone or anythng else does. I think this is often condensed by saying that God is without passions.
I John clearly states that God is love. For God to be love, he must be loving someone. But if he has to have “others” to love, then his love is then contingent on someone or something else. So the answer to this seeming contradiction (God is love) is that God loves himself. The Father loves the Son loves the Spirit loves the Father.
God exist within himself in perfect relational unity.
Analogies consistently have big problems explaining the trinity. They usually describe something other than the Trinity (i.e. water describes modalism) Probably the best analogy the Bible gives about the Trinity is marriage. It explains that through marriage, two become one, and that this is a mystery. So how can two distinct persons be one? think about how it might be true through your union to your spouse (if you’re married).
I don’t expect the LDS church to accept this doctrine, but I would like for individual saints to have a better understanding of why we Trinitarians believe this doctrine.