Background: Yes, this is relevant, sorry it's so long. Long ago, there were only two dragons, Curse and Regis. Curse was the first Dark Dragon, and the first male; and Regis was the first Light dragon (and the first female). The two did not mate; for while Regis chose the way of peace, order, and virtue, Curse chose the way of violence, chaos, and evil.
These dragons soon came to two powerful magical constructs (formed of warped reality, or discord, which is the driving force behind magic): the Source Crystal and Neosis Gem. The Neosis Gem was a giant diamond capable of generating and harnessing creative energy (AKA creating more dragons), while the Source Stone was a giant stone that would channel the Neosis energies, making each dragon created by the Gem reflect its creator and yet be genetically unique.
To make a long story shorter, a third being, as powerful as Curse and Regis, also sought the Gem and Stone and when it couldn't have them it went kamikaze and killed not only the two (battling) dragons but itself as well. The subsequent release of magical essence inadvertently melded and went into both artifacts, and thus the dragons were born.
Each dragon reflected their harsh origins; since Curse and Regis were both forceful creatures and felt the need to fight for their beliefs (and to prove their dominance; they're dragons after all), so do their spawn. Because of this, the early dragons were very warlike creatures, and their world became a war zone. This belligerence was inherited by modern dragons, along with their ancestor's courtship rituals.
Since dragons prized power and fighting prowess, it didn't take long for dragons to unanimously decide that one's would-be mate would have to prove him- or her-self by defeating (read: subduing, overpowering) them. This led to dragons seeking powerful/skilled mates since no one wanted a weak mate; no, no, the thinking went; the harder the fight required to earn the right to mate with someone, the better they'll be as a mate!
This wouldn't really be a problem, but due to in-story reasons, all dragons are A) capable of becoming human and B) all learn they can become human from the moment puberty starts unless already informed.
The Problem: Since dragonslayers are elite warriors who are employed for the sole purpose of subduing, overpowering or slaying dragons, they will (almost) inadvertently become attractive under the dragon's courtship rules. Sure, sensible dragons will stay away, but most dragons aren't sensible-natural selection favored those crazy enough to take on powerful members of the opposite gender, those who'd be difficult and even dangerous to court, and modern dragons reflect that.
Modern dragons have also inherited a martial code, which leads them to respect those who can rival or exceed their own level of power or skill, which only worsens the problem. "But wait," you say. "Is this really a problem?" YES.
Most Dragonslayers are Male Due to this being (somewhat) realistic medieval fantasy, sexist attitudes and cultural expectations make men naturally more like to be dragonslayers. Being a dragonslayer also requires a certain amount of recklessness (AKA guts, courage), which I know from personal experience men are more likely to have. And men aren't exactly known for rejecting women's advances, in any era.
Veteran Dragonslayers Aren't Idiots This is pretty much self-explanatory; in order to become a veteran dragonslayer, a "pro" if you will, one needs to have a certain amount of brains, common sense, foresight, and critical thinking ability. Accepting a dragon's advances comes with a lot of benefits, while rejecting them comes with very few benefits;
Having children with a dragon results in more powerful and capable children, and greatly increases the chance of said children having magic;
If one accepts a dragon's heart, they will gain the ability to do magic (Ex: pyromancy for a fire dragon), or gain stronger magic if they have magic already (see, 1 out of 14 dragonslayers are mages);
It usually results in one having a dragon companion, which is useful for obvious reasons (transportation, powerful backup, and so much more)....
and of course, "hell hath no fury like a woman scorned" applies tenfold to dragons. After learning all this from their seers, the king would like to know How Can A King Best Deal With Draconic Courtship Practices?
The king is looking for the best way to handle this, as it appears that this will put dragonslayers in a position of power and therefore make them a threat to the system (AKA him and his noble supporters). He specifically wants a solution that he can implement that will: A. Ensure and maintain society's stability and B. Prevent dragonslayers from abusing this quirk of dragon culture to their benefit and his detriment; ie. balance this so they don't get overpowered.
If two half-dragons have a child, the result is a Dragonborn, a human who is both human and dragon and represents the full potential of each. Basically 1/2 + 1/2 = 1. Thus Dragonborn + half-dragon =1 1/2, half-dragon + human= 1 1/2. That's not to say the results are the same, however.
A Dragonborn & half-dragon pairing results in a Dragonborn that's a little more (specially 1/2 more) human, making them more spontaneous, adaptive, artistic, and intellectual than a regular Dragonborn.
A half-dragon and human pairing results in a human that has 1/2 dragon thrown into the mix, making them more passionate, aggressive, impulsive, and stubborn than a regular Dragonborn.
As always, I appreciate your input and feedback, so if you decide to VTC or downvote, please let me know why so I can improve this question. Thank you!