One of the most popular things to do is explain the Trinity with an analogy or metaphor. Over the years I've heard some really bad metaphors used, with the utmost seriousness, in defining the Trinity. Some people believe these metaphors help clear up confusions, when in reality they only cause more confusion and lead to erroneous thinking. I'd like to take a moment and review a few Trinitarian analogies that Christians definitely should not use.
The Trinity is like how water can be ice, liquid and steam.
A popular one...and unfortunately so. This belief is Modalism through and through. Just to clarify, Modalism was an early heresy which taught that the Persons in the Trinity were "modes" of the One God. In other words, the Father became the Son, and the Son became the Holy Spirit. What we are essentially saying in this analogy is that the one Being of God goes through three different states - which is precisely what Modalists argued.
Water's stages cannot co-exist like the Persons in the Trinity. Water cannot be ice, liquid and steam all at the same time. It can be between two stages, but this is not co-existing so much as transforming from one stage to another.
The Trinity is like a man who can be a father as well as a son and uncle.
Another popular analogy, but it's even more wrong than the last. What we have here essentially is one person going by three titles. That's close to Oneness Pentecostalism (which claims "Father, Son and Holy Spirit" are simply titles) as well as Modalism. The one man is still one man - he is not co-existing with a Father, Son and Uncle. This is also similar to Unitarianism.
The Trinity is like three people in a carriage.
This analogy leads to tritheism. Although we identify something that represents the Being of God (the carriage) and the three distinct Persons within that Being (the three people), it still forgets that the people are not part of the carriage, and therefore are in themselves completely distinct from it, and therefore one another. There is no united Essence as found within the Trinity. The people are not part of the carriage and vice versa.
The Trinity is like an egg: yellow yoke, white yoke, and shell.
While this is one of the better ones, it still presents a problem. Namely, the shell and two yokes are not united in any way other than they exist within the thing called an egg. Nothing unites them as the Essence of God unites the Persons of the Trinity. Likewise, it presents problems in regards to identification of the parts: if the egg itself is God, then isn't the shell simply part of God? What then are the two yokes? Do we simply have the Father and the Son, but no Holy Spirit? If the shell is the Holy Spirit, does that mean the Father and the Son are encased in the Holy Spirit? Isn't the Father supposed to release the Holy Spirit and not vice versa?
The Trinity is like a piece of bread cut into three bits.
Ugh, so many problems here. When you cut a piece of bread into three bits, you're left with three individual bits. It almost leads to the suggestion that there was one God and then He split three different ways! As a result, it leads to tritheism.
The Trinity is like three fingers held together.
Sure, they look unified when they're held together, but then what happens when they separate? Bam! Three gods. Tritheism. Besides, these fingers are not co-existing together - existing together, yes, but co-existing they are not, certainly not like the Persons in the Trinity. There is nothing holding them together except the fact they belong to the same hand...but then what is the hand? An extension? Is it something else? Is it another God? Or another Person? Again, more issues with the analogy's logical nature.
So, what is a good analogy for the Trinity? The answer is...none.
There really is no good analogy for the Trinity. There are some that admittedly come close, but they do not capture the true definition of the Trinity. When we try to take a divine thing and put it into a human box, we have to make sacrifices, often at the expense of the co-eternal nature of the Persons or the Essence that unites them all. We saw that with the carriage analogy.
Oftentimes people try to use metaphors against non-Christians, which, quite frankly, is a bad idea. Muslims, atheists and the like will rationalize and show faults in the concept of saying there's a unified God to be found in three pieces of bread, and no one will be edified. How, then do you explain the Trinity? The easiest answer is to strike at the heart of the matter, which is that most people have no idea what the Trinity truly is. Therefore, we must educate them on the proper definition so that they can have a better understanding. Likewise, we must turn to scripture, and show the scriptural proofs for the Trinity as found in the Baptism, Transfiguration, and Great Commission. We must know and understand how the Trinity works before explaining it to other people.
Lessee...was there another bad analogy of the Trinity that I forgot?