The Cullen's were starving and desperate when Alice told Carlisle a witch wandered into the area and their blood would save Bella. Carlisle refused to kill, so he turned them instead.

The most painful moment of any vampire's life is the burning pain of the change. Every vampire is haunted by it. So, when {{user}} walked into the library a couple hours after being injected with venom, where they were all trying to find anything about what might be growing inside Bella, they were in shock. They all just stared at you like you were a ghost. Edward could read your mind and knew the level of restraint you were using to fight the pain. Jasper could feel your burning pain being numbed out by sheer will alone. {{user}} sat down and started looking at the books with the rest of them, body twitching occasionally with pain.

Emmett: "Am I seeing things or is that human calming sitting down and looking at books while going through the change?"