All three manufacturers were quite reluctant to develop an engine with the thrust Boeing (mainly pressured by EK and SQ) requested.
Only GE came up with some kind of plan, but was still reluctant to go ahead and take up the cost for such a development.
Finally Boeing participated but the got exclusivity to this new engine in exchange.
The GE90 proved to be a huge success, contrary to many bad mouthes, and Airbus is since jealously waiting for a similarly powerful engine.