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3 dragons is nice. 100 dragons is better.

Is there some kind of reason that Daenerys is not breeding more dragons and taming them? Of course it costs food but it also gets more knees bent (because everybody in Westeros seems to have stiff knees), infact it turns them into jello.

Dragons can change their gender and as such don't have a true gender. Apparently certain Dragons are known to have been thought of as male or female though it is not known as to whether they kept the same gender for the whole of their lives.

Dragons are neither male nor female, Barth saw the truth of that, but now one and now the other, as changeable as flame.
_{A Feast for Crows: Chapter 35, Samwell IV}

For dragons to breed it appears a "female" lays eggs and then a "male" has to come along and fertilise them.

Now onto the question as to why they don't breed now as it appears they should be able to. Note that Dany's dragons are still very young only a few years old. It is possible that they just haven't developed the organs needed to breed yet.

The whole process around dragon breeding appears to be shrouded in a bit of a mystery but we could also speculate that dragons don't like to inbreed but I doubt that is the case.

^{Most of my information is from memory or this wiki link.}

We don't know a lot about dragon's reproduction

Still, dragons can live way older than humans, and may lay several clutches during its lifetime, but not that frequently (otherwise, the dragons would not be extinct). Dany's dragons are young, give them time.

Breeding more dragons

Technically they should be able to breed eventually.

A common misconception is that Daenerys' dragons are all males. That is not true.

Dragons do not have a fixed gender¹. They can change from male to female, and vice versa, at will.

What fools we were, who thought ourselves so wise! The error crept in
from the translation. Dragons are neither male nor female, Barth saw
the truth of that, but now one and now the other, as changeable as
flame. The language misled us all for a thousand years. Daenerys is
the one, born amidst salt and smoke. The dragons prove it.
_{AFFC - Samwell IV}

But we do not yet know when Dragons become capable of laying eggs and reproducing.

Daenerys' dragons are a couple of years old, so they could be considered children among a species which lives for centuries.

Presumably, they should be able to start reproducing at least after 10-20 years. Syrax was born in reign of King Jaehaerys I (Implied as Rhaenyra who was born in 97 AC during reign of the Old King and named the young dragon, which implies it was a hatchling and had no previous rider or name). It grew up during reign of King Viserys I and known to have laid eggs during that period. Viserys reigned from 103 AC to 129 AC for 26 years. If we assume that Syrax was born in 97 AC² (As it existed back in the day of Jaehaerys I), Syrax must have been at least 10-20 years old when it first laid eggs in reign of King Viserys. It can't be emphasized enough that this is merely my speculation, Syrax could have been younger (could be more like <10 but that seems wrong given that dragons must have some stage in their early life when they are incapable of reproducing like all animals).

The secrets of Dragonkind were lost when King Baelor ordered Septon Barth's Unnatural History to be burnt through out the Kingdom. So as of now, their nature is a mystery.

So in conclusion, while Dragons are not barred from breeding on account of their gender, they are apparently not breeding because they are still very young and can't actually breed just as yet. This is however an opinion, the real answer would be "We do not know" as of now.

_{1. There are those who dispute it but Barth was the leading expert in Dragonlore in Westeros and he actually had a first hand chance to observe dragons during reign of Jaehaerys I. Maester Aemon is also a great scholar and if he agrees with Barth instead, So do I. Munkun only saw the extinction of Dragons and the only Dragons he ever observed were sickly and dying. Thomax on the other hand, we do not know when did he live so we can't speculate on accuracy of his views.}

_{2. 97 AC because that's when Rhaenyra was born, during the reign of Jaehaerys I. It was a custom of Targaryens to lay dragon eggs in cribs of new born Targaryens, and it would hatch and grow with the child.}

In the short term, we can't say for sure. In fact, it's possible one is pregnant now, how would we know?

Regarding long term breeding, 3 individuals is probably below the minimum viable population for Dragons. Below that level, you eventually get inbreeding, which seems to be what happened to the dragons in Westeros.

https://www.britannica.com/science/minimum-viable-population

Is there some kind of reason that Daenerys is not breeding more dragons and taming them?

How would she get the eggs to hatch? Remember that last time it required the sacrifices of both a king and a witch to hatch the eggs. Perhaps that was because the eggs were older. But even with fresh eggs, hatching requires fire and sacrifice.

It is possible that the sacrifice must be a loved one of the person making the sacrifice. Certainly Drogo and Rhaego met that criterion. And the witch was someone that Daenerys had saved from death. Daenerys had trusted her and been betrayed. She may have counted enough for those purposes.

If Daenerys is the only one who could make the sacrifice, she would have to deliberately sacrifice someone she loves to hatch a dragon. That's only about five people. Maybe it could grow to ten. Certainly not a hundred. I don't think that it's possible to fall in love with someone just to have someone to sacrifice.

1. Jon Snow.


2. Jorah Mormount.


3. Grey Worm.


4. Missandei.


5. Daario Naharis.

I'm not sure that Tyrion Lannister or Varys count at the moment, although they might get there. I guess that Daenerys killing herself might work.

If we expand out, Jon Snow loves more people and might be able to hatch a dragon. Presumably his wolf counts, his three cousins, and people like Sam. If Tyrion is secretly Aerys' bastard, then he might be able to make sacrifices. Possibly Jaime, Bronn, and a couple others.

So assuming the dragons are old enough to reproduce, it's not clear that they actually could do so without sacrificing someone. Perhaps if they had a dragon egg, they could have hatched it from Viserion's death. But hundreds of dragons seems unlikely, given the cost.

Why didn't previous rulers hatch hundreds of dragons? It's an expensive act. We don't know what it might cost to produce eggs. But we do have some measure of the cost of hatching them. And it's not the kind of price that someone can pay lightly. Perhaps Stannis was willing to sacrifice his daughter for power. But it doesn't seem like the kind of thing that Daenerys and Jon would do.