game of thrones - Why aren't the dragons busy making more dragon babies?

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.

Answer

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.

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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.

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