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antisprog
If they do mean it, it's only because They see their spawn as extensions of themselves rather than genuine individuals

I bet dollars to donuts that if their "beloved" spawn tried to assert themselves as an individual or do anything that the breeders don't like such as choosing a different life path/career, marrying someone of a different race/culture/religion ,refusing to have children or gods forbid come out as gay/trans/gender nonconforming , those same breeders would disown them in a New York minute ("I love my kids" be damned)

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Cambion
This isn't as uncommon as you might think. I've heard plenty of breeders in various sub-Reddits say they hate everyone else's brats, but their own sprogs are special and therefore the exception. I mean I guess that's good they at least care about their own kids - some parents don't even care that much.

Or in some rare cases, the person who likes their own kids may be a legitimately good parent and has raised a child that doesn't completely suck, but then they have to deal with the brats of other people who are incompetent breeders.

But then I question if they genuinely mean it when they say that, or if they only say that because they are obligated to.

Still, odds are good that narcissism is involved to an extent lke you said. People like their own little reproductive DIY projects more than other people's because they contain the parents' surely exemplary DNA.