Ways to Challenge An Argument in Logic

Two common ways to question an argument in logic: 1) challenge the argument's premises; 2) supply counterexamples that call into question the argument's validity. In logic, an argument technically has premises and a conclusion; without premises or a conclusion, statements are not arguments. Another feature of arguments is that when we're talking about deductive arguments, they're either valid or invalid, sound or unsound, not true or false. Statements or premises can be true or false, but not deductive arguments.

Take the following argument as an example. I'm going to make it a theological argument due to the blog's focus:

1) If Christ is the Son of God, then Christ is God.
2) Christ is the Son of God.
3) Therefore, Christ is God.

The argument is formally valid: it reasons that if p, then q in the first premise; the second premise affirms p, and the subsequent conclusion is q. It's an example of modus ponens and the conclusion simply is a deductive inference of premises 1) and 2). Yet there is a different point I'm trying to make in this case. How can I challenge this argument by employing the principles of logic?

First, I could question the premises. Why should I think the first premise is true? An adherent of the Trinity might try to convince me that 1) is true but the point is that I could challenge it: I don't have to accept the premise. Secondly, I could produce a counterexample to show that it's conceptually possible for the argument in question to be invalid. Producing counterexamples can become a complex and difficult process, but I want to keep it simple.

Counterexample:

1*) If Adam is the Son of God, then Adam is God.
2*) Adam is the Son of God.
3*) Therefore, Adam is God.

I would like to get some thoughts from Trinitarians or some logicians on my counterexample, but even if we abstract from 1*) and consider the premise to be questionable--it is no more questionable than 1) above and 1* is a hypothetical statement, not an indicative utterance. However, 2*) is true, according to Luke 3:38, and I don't think any serious Bible student would deny that the Gospel of Luke identifies Adam as God's Son. Yet the conclusion (3*) is false: Adam is not God since he is a creature and there is only one God in Judaeo-Christianity, that is, one Supreme Being (Deuteronomy 6:4; Isaiah 42:8; 45:5; Ephesians 4:5-6; 1 Timothy 2:5). Ergo, 3*) does not follow necessarily from 1*) and 2*).

The point of this exercise has been to illustrate how one can challenge arguments in logic. To review, the two main ways are questioning the premises of an argument and producing counterexamples to show a deductive argument is likely invalid. We want to show that the conclusion of an argument is not necessarily true and may even be false, or the argument as a whole could be invalid.

See https://www.bu.edu/wcp/Papers/Teac/TeacLave.htm