How do you think Morgoth created deagons?
Morgoth didn't have the abbility to create things out of the blue (the only one who can do that is Iluvatar). How do you think he created dragons?
I haave a couple of theories:
1) Dragons are, like Balrogs, corrupted Maiar. But I don't think this is possible.
2) Morgoth used his own essence to make them, hence why they're evil and greedy by nature.
3) They were once Yavanna's creatures but then were corrupted by Melkor.