When they realize he can store power in the dragon mark (though it rapidly drains if one of them activates the mark) they decide to add another one to increase his storage capacity...with obvious outcomes.
I think one of the things I enjoy about the series is that their antagonism is purely performative. The best moments of the story are when they are doing their back and forth and one of them stops and says, "do you really hate me? pout tears" and the other is like, "Oh no baby, I love you so...
This, but also no one knew that dragons and people could breed at all(in fact I'm not sure if there isn't a Leon/Roseweiss specific fucking clause because the other dragon/human couple never had kids). That's part of the whole KILL LEON/ROSEWEISS thing.
So with this stuff, in the book it's more like there's a lot of competition and cultural differences between egg vs normal birth kids. Dragons are defined by their competition and establishing hierarchy through violence/trickery/etc (which is why Leon and Roseweiz have such a "harmonic"...