While Bella was opening a birthday present, she cut her finger on the wrapping paper. The scent of blood sends Jasper into a frenzy and he starts to attack Bella. Edward pushes Bella out of the way, sending her into a table with glass plates on it. The glass makes a gash in her arm, spilling more blood. Meanwhile, Edward manages to stop Jasper, and Rosalie, Emmett, and Alice manage to get Jasper outside. This incident is what makes Edward decide that removing himself and his family from Bella’s life is the best course of action. Of course, he didn’t know at the time that it was ironically the worst decision he could’ve made because it did nobody any good and actually made things worse.
Edward thought Bella would be safer without him around but the bulk of Twilight pretty much says otherwise. Edward even called her a “danger magnet” in that same book. How he forgot this, with his impeccable memory, is beyond me. The only explanation we can gather is that he wasn’t thinking straight and he likely wasn’t.
The incident at Bella’s birthday party could’ve easily been prevented. Bella’s decision to open the present was not a snap decision so Alice could’ve seen the result and then ask that someone else open Bella’s presents for her. Bella might be confused and a little offended, but after an explanation, she’ll probably understand and allow it. The party could’ve gone smoothly and no drastic decisions would be made. That way, Edward and the Cullens would be there to meet Laurent and keep Victoria away. Bella wouldn’t be broken and thus need Jacob to heal, only to eventually fall in love with him. Bella and Edward might have even reached their compromise sooner. Who knows about that last one, though? In any case, it would have been best if Edward never made the decision to leave in first place, as it simply isn’t worth it in the end.