Sacred Haven of Debauchery

Because each of us wants to ensure the survival of our own genes; other people's children are carriers of other people's genes and competitors to our children, and that's natural.

Sounds like Freud. People don't care about the survival of genes. I'm serious. Indirectly, yes – in order for genes to survive, certain instincts appeared in humans. Self-preservation and love for offspring, for example. At the same time, I doubt that a person can effectively distinguish, at an unconscious level, which offspring carries their genes. It's all about habit, adaptation... If a baby is switched in the maternity ward, the mother will most likely not suspect anything. Other people can consciously take in another person's child and raise them as their own. If all these cases are possible, I don't see what mechanism could cause unconscious aggression towards other people's children compared to their own (unless it's an immediate defense of their own children). Perhaps something like that exists deep in the brain, but I don't believe it has much significance compared to other factors.
And in any case, genes cannot be the cause; we would need a gene sensor in our body for that. At best, there's a correlation.

Their own children cause such outbursts because they are annoying.

I would even say "their own children and other people's children – are like any other people." Seriously, what do children have to do with it? Has the author of the question never had outbursts of aggression towards adults? The difference is purely at a psychological level; some people love children more (because they are cute, naive, etc.), some love adults more (because children don't know how to behave, or they are not very smart, but you can talk to adults), and some don't love anyone. Always your point, Captain.

Because family is generally an unnatural phenomenon for humans as animals.

A statement that requires proof. There are many examples of "families" in the animal world, so it is not universal.
It is more accurate to say that the subconscious-instinctive in humans is also not universal for the species and depends on the individual. If there were absolutely nothing like that in the subconscious of people, I'm not sure it would be such a common practice. But the many examples of deviations from the practice of maintaining a family suggest that it is not easy for everyone. And the subconscious-instinctive in this regard is often one of the most important factors, and I agree with that.