It's hard to think about creating a whole new life, so we help ourselves to metaphors. For example, we say that creating a child is giving him or her "the gift of life." It's a charming and poetic phrase, but is the metaphor apt? Is creating a child like giving a gift to someone?
It's important to think about it, because whether you do or you don't think about procreation in these terms makes a difference. One difference it would make if you did think procreation bestowed the gift of life is that you would probably feel impelled to have more children. Bryan Caplan makes that explicit in his enjoyable and interesting book Selfish Reasons to Have More Children, writing, "To deny the gift of life to a child who would have made your life better is a tragic missed opportunity." He seems to allude to a double tragedy here—one for you, and one for your child. The child you would have had, if you'd had one more, will tragically go without the gift of life. He or she will be forever trapped in the closet of non-existence. Or is it a cosmic orphanage, from which the non-existent can never escape? Whatever it is, Caplan is implying that it's tragic to be permanently stuck there, not having been given the gift of life.
If you really thought parents gave their children the gift of life, presumably it would be an incredibly valuable gift. If we've given our children the gift of life, they would presumably owe us a debt of gratitude for the rest of their lives. In fact, cultures that see children as strongly indebted to their parents may take that view partly because of the assumption that the very existence of a child is a gift given to the child by the parents. The Confucian Xiao Jing ("Classic of Filial Piety") says, "The son derives his life from his parents, and no greater gift could possibly be transmitted." Right after that, there are sentences about the son's profound duties to his parents. And those duties don't just have to do with care once parents are very old and in need. They would probably include the duties of young children to obey their parents and meet their expectations. The notion that life is a gift from parents would shape the entire parent-child relationship.
So yes, it matters whether life is really a gift that's given to us by our parents. Let's think about this from the point of view of Larry and Linda, who are contemplating whether to have children or remain childless. To take seriously the idea that life is a gift, you could take it seriously that there are merely possible people. Maybe the closets and orphanages I referred to earlier are fanciful, but possible people could (just conceivably) be the recipients of your gift of life. Then again, on further reflection, how could that be? Possible people are (of course!) just possible. Arguably, I can't give gifts to a possible daughter; I can only give gifts to actual people.
Now, you might think we're reaching this conclusion because we're focusing on the wrong recipient for the gift of life. We don't give the gift of life to a child who's merely possible, but to a child who will exist. When Larry and Linda think about whether to have a child, they should visualize someone in the future—"Larrinda"?— with a speech bubble that says "Please have me! I want to live!" If there are no possible people, you might argue future people are actual—or at least will be actual. Right? There will be people in 100 years (we hope!), so there are future people.
Okay, but which future people are there? It's cheating to assume Larry and Linda's future child, with that beckoning speech bubble, is one of them. For them to picture the future that way is for them to assume they've already made their decision. But they haven't. And so it doesn't work to try to shift from possible people to future people as the recipients of the gift of life.
I don't think there's any coherent story in which Larry and Linda, before they've conceived a child, can coherently think they would bestow the gift of life on someone if they decided to have a child. Creating a child doesn't have the structure of gift-giving, which requires an x and a y, such that x gives a gift to y. A kidney donor gives the gift of (additional) life to a recipient, but when we speak of prospective parents giving the gift of life to their children, we're in the land of poetry.
Caplan, Bryan. Selfish Reasons to Have More Kids: Why Being a Great Parent is Less Work and More Fun than You Think. New York: Basic Books, 2006. The "gift of life" sentence is on p. 12.
Anonymous. The Classic of Filial Piety (Xiao Jing). Translated by James Legge. Online. The quoted passage is in section IX.