I sided with The Blades, i know maybe it is not a popular stand here but i have my own thought about it. This game always play illusion even at the very start about who's bad and who's good. We are about to be executed by the Imperials but later turn out to be they are the good guys, aren't they? But that is not the issue...

So i used the similar device in this case

Delphine may look bossy and have some attitude, but she never do the Dragonborn wrong in anyway. If anyone want to use "why she don't do everything herself?" argument, i simply say she is a quest giver like any other NPCs, the player who must do all the things in this game. And there is a part of bad game design in it like how she get passed the mechanism in Jurgen Windcaller tomb, the Dragonborn must use Whirlwind shout to get pass it, but i blame Bethesda for that.

About killing Parthy...well let see...

If i am an immortal bad and evil boss, only the superhero can kill me. Lucky for me that superhero don't have any idea about me and what is going on, and that superhero is searching a way to kill another bad and evil boss out there, my rival... so why not i make friend with that superhero to make sure he/she will not kill me? It is logic isn't it? I will even tell a part of my secret to gain trust. After he/she manage to kill my rival, i just wait for him/her to die, because i am IMMORTAL and only he/she can kill me...later i will go rampage and bring destruction on earth with no problem

The same goes to Parthy. He know about the prophecy, he wait for the Dragonborn to come, make friend, gain his/her trust, let he/she kill Alduin, then wait him/her to die. That is why he wait for thousands of years...he's pretending.

If you guys realize the Greybeards are useless and they have evil agenda...yes they did teach you somethings, but they hold back many things. They claim the Dragonborn is not ready to meet Parthy but actually they fear Dragonborn will kill Parthy. They don't even tell that their leader is a dragon. Now think, at the first time the Dragonborn meet them, that is after learning Whirlwind Sprint, the Dragonborn have no idea at all about his/her job is killing dragons and absorb their soul whatsoever. You guys see that? They don't tell you what is Dovahkiin/Dragonborn because they FEAR. Even after the Dragonborn have learn the complete Fus Ro Dah, they mislead the Dragonborn to protect Parthy. ANGEIR EVEN DON"T Care if the world is destroyed because he said that maybe the world is like an egg, it will give birth to the new world. You see how crazy and twisted they are?

While Delphine who really tell Dragonborn what being a Dragonborn really is.

It is in Alduin Wall prophecy remember? The last part of the prophecy is the Dragonborn hailed by The Blades, and become their leader.

So, if you don't kill Parthy, you are against the prophecy, when you against the prophecy, you are the BAD/EVIL/TWISTED/FALSE Dragonborn