Illustration in natural world that leads to understanding of supernatural. The logic of analogy.
There are actually fish in the sea of Galilee which pick the fertilized eggs off the sea floor and hold them in their mouths until they hatch. Some use this to prove that this was not a miracle. But the response to that is how did Jesus know that that particular fish had a coin in its mouth, that Peter would catch the right one and how did he know its denomination or amount.
It seems that Jesus had not been at the Passover - perhaps up in Gentile territory. Therefore he wasn’t around to pay the tax. When the temple tax collectors ask if Jesus pays, Peter’s impulsive response is, “Yes, he does.”
Royalty goes free. Sons are exempt. They don’t pay taxes. This is a political / kingdom illustration, but we are not talking about kings and taxes and politics. This is a religious issue - temple tax. Who pays the temple tax? All the citizens of Israel. Who goes free? The Son of God. After all the temple is God’s House.
Jesus didn’t have to pay the tax. What is the claim? His deity for one and that other believers are exempt too.
Jesus pays the tax just to avoid offending, but He’s already made His point. This is yet another instance where we see that the old system is finished and Jesus disengaging from Israel.