The Procreation Asymmetry consists of these two claims together:

1. it’s bad to bring into existence an individual who would have a bad existence, other things being equal, or the fact that an individual would have a bad existence is a reason to not bring them into existence; and
2. it’s at best indifferent to bring into existence an individual who would have a good existence, other things being equal, or the fact that an individual would have a good existence is not a reason to bring them into existence.

If existence can be an existential harm (according to 1. in the asymmetry), why can’t it also be an existential benefit? I.e. why should we accept 2.? If it’s worse for people who regret being born (or whose suffering outweighs their happiness) to actually be born, isn’t it better for people who are grateful for being born (or whose happiness outweighs their suffering) to actually be born? These are two immediate replies to the procreation asymmetry, and providing a satisfactory response which does not rely solely on intuition (from hypotheticals) would better make the case for the asymmetry.

I think it’s very likely that what I say here isn’t at all original; it’s probably come up often in defence of the procreation asymmetry. However, this thinking has been somewhat useful to me in defending the procreation asymmetry without just accepting it from intuition. It's roughly based on Johann Frick’s defense of the Procreation Asymmetry:

“Conditional Reasons and the Procreation Asymmetry”

“'Making People Happy, Not Making Happy People': A Defense of the Asymmetry Intuition in Population Ethics”

There is indeed a sort of asymmetry in the situations that can be used to defend the Procreation Asymmetry, without just referring to examples. I illustrate it here:

Consider the above graph, and suppose an individual can exist with a positive existence, exist with a neutral existence, exist with a negative existence or not exist at all. In the graph, the arrows represent when the individual in the given state would strictly (all-things-considered) have a stronger interest in being in the other state. So, if there’s an arrow which points out of the current outcome A, then A is dominated by the outcome B the arrow points to, from the “point of view” of outcome A (or the point of view of the individuals in outcome A). If an outcome is (all-things-considered) dominated by another in this way and there's no stronger (all-things-considered) domination in the exact opposite direction, it is not stable (in something like a game theoretic sense), and it’s impermissible to choose over the more strongly dominating outcome. You should not choose an outcome A that, after occurring, you’d expect (the aggregate of individuals in the outcome) to have a stronger interest in another outcome B, if the individuals in that outcome B don't have an even stronger interest in A. This is basically regret minimization, and it’s pretty similar to antifrustrationism.

Other outcomes may of course be impermissible to choose for other reasons.

Here are the arguments for each arrow, pertaining only to the interests of the individual whose existence we're considering:

1. If the individual would come to exist and have a negative existence, it would have been better for them to not have come to exist at all in the first place (e.g. they may prefer to not to have come to exist). Because they would exist, they have interests. So, there is an arrow from Negative existence (bottom left) to Nonexistence. This defends claim 1 in the Procreation Asymmetry.
2. Nonexistent (and never existing) individuals have no interests in coming to exist, since they have no interests at all, because they have no point of view (and, if they don't come to exist, they have no preference to exist). So, there is no arrow from Nonexistence (the right side of the graph) to Existence (the left side of the graph). This defends claim 2 in the Procreation Asymmetry.
3. Existing individuals also have an interest to be at least as well off as they are now or strictly better, so there are arrows going up in Existence.

Furthermore, those who do exist often prefer to continue to exist and may have interests in continuing to exist, so ending an individual's existence may be a harm. However, once they stop existing, they no longer prefer to exist and any such interest disappears.

Our obligations to others are, in this way, conditional on their existence: if they don’t come to exist, they have no stake in the outcome. Existence can be understood in a narrow or wide view way: in a narrow view, identities matter, but in a wide view, they don’t. The Nonidentity Problem is a classical illustration of the differences between these two views.

This argument is essentially comparative. Whether or not you must give up the independence of irrelevant alternatives (which is the claim that the ranking of outcomes does not depend on what outcomes are possible, so if A < B given for a given set of outcomes, then A < B for any set of outcomes) depends on which other outcomes you’re allowed to compare to, e.g. only realistically probable alternatives or also hypothetical ones. If you accept the asymmetry and are willing to give up the independence of irrelevant alternatives, you may find the following utilitarian approach for comparing outcomes intuitive:

“Person-affecting views and saturating counterpart relations” by Christopher Meacham (Also here)

His approach is to measure the harm in an outcome with respect to a set of outcomes as the sum of the differences between an individual’s maximum utility and their utility in the given outcome, using 0 if they don’t exist in the given outcome, and then minimize this harm. He then extends this approach to cases with different individuals (different identities) through “saturating counterpart relations”, taking a wide view of existence.

Meacham’s approach also solves the Nonidentity Problem, and avoids the Repugnant Conclusion and a specific principle of Antinatalism, which I define as the claim that it would be better for anyone who would come to exist with non-maximal utility to not come to exist at all, other things being equal. Note, however, that other things are rarely equal in practice, since in realistic scenarios individuals will have effects on others. This particular Antinatalism principle does not imply that we generally should not have children in practice (even considering the probabilistic risks of them having a bad life), because there may be other reasons why having a child is good, e.g. they may have positive impacts on the wellbeing of others.

Otherwise, if you aren’t willing to give up the independence of irrelevant alternatives, but still accept the asymmetry, then this leads to the principle of Antinatalism defined above. This is because for any individual with non-maximal utility, we can imagine the same individual (or, if the Nonidentity Problem is solved, another hypothetical individual) with higher utility, and that would be strictly better (a weak assumption), and by 2 of the Procreation Asymmetry, no better than not coming to exist at all, so by transitivity (and the completeness of the order, both weak assumptions), not coming to exist at all would be strictly better.