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I think an alternative explanation below is more interesting and even more relevant to David's motive.
In the scientific-research stage of Project Genesis, it was revealed in this movie that Dr. David Marcus (at least) used proto-matter. Saavik was stunned when David revealed this fact to her in the movie since proto-matter was banned by the scientific community as being too unpredictable. Kirk's son made the excuse that using the contra-banned substance helped solve certain problems in the project.
God made creation for us to prosper in, to love and to be loved. There are almost an infinite number of things that we could legitimately do, with relatively fewer things that God forbids us to do. The main forbidden fruit is to decide for oneself the criteria for good and for bad apart from God. That's God's domain.
In the Genesis story of the Judea-Christian Bible, the forbidden fruit tree in the Garden of Eden represents this knowledge. God said of it, "The LORD God gave the man [Adam] this order: You are free to eat from any of the trees of the garden except the tree of knowledge of good and evil. From that tree you shall not eat; when you eat from it you shall die." (Genesis 2:16-17)
In The Genesis Device's development, when David took the shortcut in using proto-matter, he took to himself the prerogative to decide what was acceptable and unacceptable, or perhaps decided that there is neither criteria for good nor for ill.
Just like when Adam and Eve ate the forbidden fruit in the Book of Genesis, in what Christians call "The Fall", they did not die right away, it took some time before David took the fall for his actions in Project Genesis. In a similar way that Adam and Eve were thrown out of the Garden of Eden for eating the forbidden fruit, once the forbidden proto-matter did its dirty work, the Genesis Planet creation essentially threw David out of paradise to his death.
David realized that none of the events on the Genesis planet would be happening at all if he had not eaten the proto-matter forbidden fruit. He must have thought that it was a just act to volunteer for the execution. He was the Fall Guy.