Why was Edward immune to papercut and not Jasper?

Question

How could Edward attend a human school (where paper cuts; and other skin damage from fights and sports is an absolutely everyday activity); if a small papercut with a single drop of blood on Bella drove Jasper totally insane with bloodlust?

For that matter, why did Edward not try to go for Bella the same way Jasper did; and protected her instead?

I took the little package, rolling my eyes at Edward while I stuck my finger under the edge of the paper and jerked it under the tape.

"Shoot," I muttered when the paper sliced my finger; I pulled it out to examine the damage. A single drop of blood oozed from the tiny cut.

It all happened very quickly then.

"No!" Edward roared.

He threw himself at me, flinging me back across the table. It fell, as I did, scattering the cake and the presents, the flowers and the plates. I landed in the mess of shattered crystal.

Jasper slammed into Edward, and the sound was like the crash of boulders in a rock slide.

There was another noise, a grisly snarling that seemed to be coming from deep in Jasper's chest. Jasper tried to shove past Edward, snapping his teeth just inches from Edward's face.

Emmett grabbed Jasper from behind in the next second, locking him into his massive steel grip, but Jasper struggled on, his wild, empty eyes focused only on me.

(Twilight: New Moon)

Canon answers only please.

Answer 1

The simple answer would be that Jasper was a savage vampire very unlike Edward & the other Cullens.(The details about Jasper's past are covered in Book 3)

Not long ago (maybe 10 years) Jasper was a member of a gang that hunted people for satisfying their thirsts. Edward on the other hand was a Cullen for 100 years. He did kill people in his early vampire life but Carlisle reformed him into a vegetarian way of vampire life. And besides, Edward, after a later realisation, didn't want to be a monster.

Edward could control his thirst for human blood because he didn't want to drink human blood. He didn't want to be a monster. He could wilfully restrain himself just like Carlisle & others. But Jasper had a different upbringing as a vampire. He hunted people until very recently & was part of the Cullen family after Alice found him. Jasper was "trying" to reform.

To answer the question about why Edward didn't react like Jasper & lunged at Bella, instead came in between the two is because his love for Bella was much more intense than his thirst for Bella's blood.
Remember also that Edwards thirst for any other human's blood is far weaker than his thirst for Bella's blood. This is clearly explained in Book 1.
Edward grew accustomed to remain between humans ie school but the moment Bella walked into class, the scent from her was too much for him to control himself & he takes off away from town with the determination to never return. But his curiosity & connection with Bella brings him back to town. In the climax of Book 1 when he has to draw out poisoned blood from Bella's body, he indeed finds the will to eventually stop & save Bella rather than killing her by drinking her blood.
So love wins over lust.

It's long time since I've read the books, the details are a little hazy, but it's all in the books

Answer 2

It should also be noted, that at school, Jasper would be concentrating very hard on exercising his will to not kill everyone in the room. At his home, he would be more relaxed and his guard would be lowered, since he doesn't have to keep up the human facade. He may not have been ready for the challenge of suddenly being mere feet from human blood in the air.