Lack of wisdom and zealotry.
While Hermione is very intelligent, she lacks the experience that people or, more generally,
beings have cultures, self-convictions, attitudes, priorities and beliefs leading to behavior which well-meaning people find unacceptable.
House elves are proud that they are "allowed" to serve wizards and witches and it seems that most of them are treated not badly (Dobby, Kreacher and Binky are the exceptions).
Dobby had very good reasons to long for freedom, Kreacher was bitter and resentful and Binky was the scapegoat for Crouch.
While house elves are fictional the behavior of humans is identical. Everyone will experience sooner or later that people really sell their birthright for a mess of pottage and you get in trouble for telling them so (and they do it anyway).
If you are confronted with the reality that the being in question does not want your "help" or even find it offensive, you may come to the conclusion that you are completely helpless. And this is a very debilitating feeling.
One option to avoid this is zealotry: Do not try to understand what the real situation is (because it could tear down your ideals), but replace it with a world where everything works as it should work in your mind.
Hermione ignored Dobby's plea that her continued preaching in the kitchen is aggravating and brings trouble for him. This is typical for zealotry: If your intentions are good, the results must be good and if it does not work out, then either the targets of your help will sooner or later convert if you are nagging them enough (wrong) or THEY (You know, those Freemasons/Jews/Pagans/Counterrevolutionaries/etc.) are responsible.
Hermione believes goodwill is enough and therefore her efforts are incompetent. Once she is willing to learn about the house elves and how they think and what they believe she is much better able to transport her message.