If Tiber Septim parlayed with Paarthanax, and let him live, and declared him off limits to the Blades, why do the current two Blades not respect that original decision and make contrary demands of us? The player is simply following in Tiber's footsteps by seeking the dragon's advise and then just letting him be.
The answer is literally because Delphine is ignorant. She simply doesn't know the history of the Blades, or of the Oath that Tiber Septim made to/with Paarthurnax.
Delphine has heard a small, moticum of information about what she thinks the Blades are supposed to do. "They kill Dragons, and when the Dragonborn comes, you will serve him and help him slay Dragons". But she has zero knowledge of the epic history or duty that the Blades are supposed to stand for.
Thanks to the Thalmor, she never will understand or know either. She is one of the only two Blades left in existence, the Thalmor having killed all of the rest. Maybe she should take some time off and go study in the Imperial Library in Cyrodiil, but alas any option to correct her and get the Blades back onto the right track will either have to wait for a DLC or Expansion, or it will never happen at all. If they aren't going to let us correct her and get the Blades back on track, then they need to remove the essential tag from the last two Blades (because I know that my Dunmer Assassin really wouldn't mind slitting a couple of arrogant, ignorant Blades throats...).
Like someone else mentioned, Delphine is very much like Astrid. She has been the unquestioned leader of the two for so long, that now when presented with an actual Dragonborn (whom she is supposed to serve), she just can't give up the reigns of power. So she is trying to use your character as a tool in her game, which she is ignorant to the actual rules that allowed the Blades to become great in the first place.
The Blades have become nothing more than a pathetic, sad joke of what they once were. They either need to allow us to fix them (a book fetch quest, return visit to Cloud Ruler Temple and Bruma, something...), or they meed to remove the "essential" tag and allow us to kill them (which will also fix the situation). Because as things stand right now, the Blades aren't even worth spitting on.
Just my opinion though...

- I'll finish what the thalmor started.
epic fail bethesda....