In the Prometheus Blu-ray menu, the summary for Quiet Eye contains information hinting a link to the Bio-Weapons Division of Weyland Industries.

Special Order 931 is the secret programming Weyland had input into David to exploit his findings on Planet 4.

When he talks about nostalgia being the enemy of science he is most probably referring to the time he spent with Elizabeth Shaw, he had to overcome the sentimentality he had for her in order to create the perfect organism.

“Sometimes to create, you first must destroy.” –Josef Stalin & David 8, Prometheus

It’s no coincidence David would quote a Dictator, he did wipe out Planet 4 in order to replace its dominant life form. He describes his creations as “Perfect” just as Weyland had described David as “Perfect”.

When he talks about the “Perfect Carriers” and the “Perfect Mothers”, it is in reference to Elizabeth Shaw. Her being Human and the most ideal union for the Ovomorph/Facehugger to produce his “Perfect Organism.”

His surprising discovery is revealed in the novelisation:

“Elizabeth Shaw didn’t die in the crash,” she said flatly. “No.” There was a tinge of reminiscence in his voice. Reminiscence, but not regret. “We had been through a great deal together. As a consequence, I held her in the utmost respect. But eventually that was lost to time and necessity. I kept her alive for quite a while. I like to think that was another testament to my creativity, although she might have disagreed. She was my most beautiful subject. David, Alien: Covenant: The Official Movie Novelization by Alan Dean Foster.