But is the really using sound logic? Or, is it a method of tricking one's mind into using one fact to prove a alleged principle that is not the actually the same principle as the fact presented, although on the surface it may appear to be so? The first statement is that "Man begets man." This is a fact, and it is stated as such in Genesis. This is often called the law of reproduction.Logic alone would tell us that the “Son” of God would possess the same deity as the Father. Man begets man. God begets God.
The claim is that since man begets man, then God begets God. I am sure that by God is meant "Supreme Being". What it is saying, in effect, is that Supreme Being begets Supreme Being because as demonstrated that a human being begets a human being. There are two things that is wrong with line of argument as related to Trinity dogma. 1) It assumes that God is under the same rules of reproduction as is man. 2) When a man reproduces, he does not beget the same human being -- the same one man -- who would be himself. Thus if the Supreme Being begets a being who is Supreme, you would actually have two Supreme Beings, not one Supreme Being.
The reality is, however, that there is nothing anywhere in the Bible that says that if the Supreme Being begets a son, that son has to be Supreme in his being. This is man's reasoning, which has to imagined beyond what is written, and actually places the Supreme Being as though he were under the reproduction laws which God has placed upon his earthly living creation. (Genesis 1:11,12,21,22,28) And to get "trinity" into this, the trinitarian has to then further create assumptions that would have to alter the logic as given to make it conform to the idea of three persons all of whom are the one Supreme Being.