The episode takes a critical turn when Geordi misspeaks his instructions to the computer: telling it to create an opponent "capable of defeating Data", rather than one capable of defeating Holmes.
Data and Holmes exist in very different ways. Data is real; Holmes is fiction (in the ST:TNG universe, of course). In order to defeat Data, his opponent needs something Data has--he needs reality. He needs to be able to affect the real world. (This is an interesting juxtaposition with salvation history. Here, the creation steps up into the world of the creator; in our world, the Creator stepped down into His creation.)
Data explains the mistake in this way: "In programming Moriarty to defeat me - not Holmes - he had to be able to acquire something which I possess.... Consciousness, sir. Without it, he could not defeat me."
Moriarty has consciousness, it seems. Does he, however, have life? If he does, he has the very beginnings of life, and he is like an unborn baby in the womb of the holodeck. He is not yet ready to leave and, so, the holodeck is the only world he knows.
Moriarty's program was a mistake. He wasn't supposed to happen. Geordi just didn't think when he created him. Additionally, the program is a threat to the "mother", to the Enterprise and her crew. Picard cannot take Moriarty out of the holodeck, but he at least can avoid throwing the baby out with the simulated bathwater. If Moriarty is, indeed, alive, then this life has as much right as the others. Even if he came about by accident. Even if he's endangering the Enterprise. Picard must try to save him.
Picard and the crew cannot "birth" him into the world; they lack the ability to give true life to him--life that can walk outside of the confines of that womb. All they can do is preserve what he has by literally saving his life--saving it to the computer, rather than terminating the program and the new life along with it.
That nearly throw-away line shines additional light on Moriarty's situation. The holodeck seems to have given him consciousness, but did it give him life? The breath of life is a mysterious thing, and while we have technology to preserve life, we cannot create it. There isn't a shortcut. The soul, that mysterious missing ingredient, is something crafted individually by God. It is, like the HMS Victory model, made by hand. That is the whole point in doing something like that.
"Before I formed you in the womb, I knew you..." (Jer 1:5a)