Alma doesn’t explain the trap, but rather simply responds seriously to the question. First, he agrees with Antionah about the basic interpretation of the Garden story. Adam was driven from the Garden. Parenthetically, the general absence of women in the Book of Mormon is remarkably underscored by the absence of Eve in this story.
Alma also agrees that had Adam been able to eat of the fruit of the Tree of Life, that he would have had continued life. He also notes that since God had declared that eating of the Tree of Knowledge would bring death, it was expedient that Adam be prevented from eating of the Tree of Life. So far, he is building his case by showing agreement with the scriptures as Antionah has cited them.
The difference between Alma and Antionah lies in the nature of death. That there is death in this world does not mean that God intended for death to be permanent. Living forever in mortality is a different condition than living forever as a resurrected being. Antionah made the mistake of limiting his vision of God’s plan.