
Why the f does she have to sacrifice so much to hold secret for a man who killed her father, steal her throne and tried to kill her loved ones?!

It's not 'hold a secret for the man' more like 'hold the secret of the man'
If the dragons know that the king is ill they're the greatest potential threat to the kingdom of Kouka. But let's not forget it also means that they're the number 1 priority enemy of the said kingdom and that they will be put down no matter what. It's either destroy your kingdom, the legacy of your blood or destroy your friends and closest allies. The 3rd option is of course to keep quiet.
I hope the author draws more of this! (●'◡'●)ノ