Why should we not believe Adam?
Why should we not believe God.
There is so much more for us in this testimony than why did Adam do what he did. We know that he was not trusting God but we cannot say why, God just doesn't tell us. But what we should glean from it, is to always trust God, no matter how things look and no matter what someone else tells us.
Gen 2:25 And they were both naked, the man and his wife, and were not ashamed.
I don't think 'naked' is talking about naked body flesh, but a naked soul. They had no sin and therefore no guilt in their conscience. So they could stand before God completely exposed, not trying to hide anything from Him.
Gen 3:7 And the eyes of them both were opened, and they knew that they were naked; and they sewed fig leaves together, and made themselves aprons.
Now they knew that they had sinned against God, their souls were no longer guiltless, and they felt the burden of that guilt. They tried to cover it themselves by their work of making the fig leaf clothing, but it wasn't sufficient. Our works are never sufficient to cover our sin or to make us righteous before a holy God.
Gen 3:21 Unto Adam also and to his wife did the LORD God make coats of skins, and clothed them.
God gave them grace and covered their naked souls and their guilt. If God had not done this they would not have been able to come before Him and their children would not have been able to come before Him, or to hear His voice calling them to repentance and salvation.
Gen 9:20 And Noah began to be an husbandman, and he planted a vineyard:
Gen 9:21 And he drank of the wine, and was drunken; and he was uncovered within his tent.
Gen 9:22 And Ham, the father of Canaan, saw the nakedness of his father, and told his two brethren without.
Gen 9:23 And Shem and Japheth took a garment, and laid it upon both their shoulders, and went backward, and covered the nakedness of their father; and their faces were backward, and they saw not their father's nakedness.
Ham was exposing his father's sin, he was his father's accuser, just as the old serpent is the accuser. But Shem and Japheth gave their father grace. They purposefully did not look at his sin and covered him in grace.
Jas 5:16 Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much.
Who would confess their faults to one like Ham, the accuser, the one who ridicules? But who feels safe to confess their sins to ones like Shem and Japheth, who will them grace, as the Lord gives grace?