I respect people as they are, and not by their tones when talking. I have an uncle, ex military, he was a rough guy, the way he talk could make people scared, and many people scared, but he's actually funny guy, very helpful and resourceful. He died already. So i can understand some people who is similar character, some people are just not good in diplomacy, we must accept that, some people may look bad in your judgment, but they are actually good people, and some people may look good in your judgment but they are actually bad person and liars
There are people who love to sweet talk to you and end up using you in their scheme, lying to you, stole your boyfriend/girlfriend, conspire against you, steal your business with smile, stab you in the back while you think they are good just by judging their character.
There are people who is sincere, they told you what you don't want to hear, their words could make your ears bleed, but they the one who help you when you are having problems, they who support you even you don't look at them, they who love you even you never bother about them judging by their character.
So, Delphine for me is sincere, truthful to you, never hide you anything, strong spirit, he think of the people even no one know her, she maybe harsh in her words but that is the truth she told you, she do her best to set your path making you know what is supposed for you to know and doing the best to set things right. Delphine and Esbern trust you, never betray you, always support you.
Unlike Greybeards who leave you wandering around not even knowing what is the mean to be a Dragonborn, they claim want to help and guide you but they tell you nothing. They hide things from you. they delude you from your path. You don't even know anything until Delphine and Esbern reveal it to you then you argue with Angeir. Afterward what you got? You got beshed by Angeir. Even though finally they give you permission to meet their leader, do they tell you their leader is a dragon? For all these time they let you kill dragons around Skyrim, but now they let you to meet a dragon without telling you that you will meet a dragon. Why not they explain to you from the beginning? You just a new Dragonborn and clearly know nothing about being a Dragonborn......It is because they fear you, mistrust you, they delude you to protect their leader and their scheme. They blame you for everything should you against them. Is it your fault trusting the Blades? Is it your fault that not trusting the one who not trust you from the beginning?
Do not get deluded by appearance....