It is not "canon" to go against the dragonborn.
I fixed it for you.
The blades hunted dragons in akavir apparently searching for something and then came to Tamriel where they did the same. In Tamriel they fought the locals too - until they were soundly defeatted at the hands of Reman Cyrodiil. Apparently when brought before Reman - a dragonborn - they declared they had found what they had been seeking and pledged their order to his service.
Even after the dragons were slain or driven out of Tamriel and Reman had passed away the blades continued to serve his descendants - the Septim bloodline.
The Septim bloodline ended with Martin Septim during the Oblivion Crisis, which left the Blades without a dragonborn to protect - but they began searching anyway just in case some offshoot of the Septim dynasty had survived in some obscure place. Then they encounter the Dovahkiin - dragonborn, and suddenly they once again have a dragonborn to lead them and to protect...
...and that's where it gets weird. Because they suddenly refuse their sacred duty on the basis the new Dragonborn isn't so big on the "let's slay all the dragons and let Akatosh sort them out" mindset that Reman held - while this might seem like a fair point, Reman was a big shot dragonslayer, bare in mind none of Reman's descendants ever so much as SAW a dragon. And the blades upheld their pledge to protect
them without any quibbles. To me this seems like a huge contuinuity hole and I really REALLY hope Betehsda notes down how nobody wants to save the blades and reflects this in TES6 instead of dredging them up to save the world AGAIN.
Or better still, recharacterise the blades as an anti-heroic faction in future DLC/games, a faction who thinks they're doing stuff for the greater good when really they're just off their rockers