The Crucible's construction manages to change the variables for the Catalyst - it creates new options, new possibilities for resolving the matter of the conflict of organics and synthetics because it will change how these things operate. Before all it could do was use the Reapers, because that was the best option it had (best by its logic, anyway). With the Crucible, it can now do something different - Destroy, Control, or Synthesis. These are a 'better' solution to the Catalyst's computer logic of 50.1% trumps 49.9%. Destroy will, by virtue of wiping out synthetics (it's always seemed synthetics based on Reaper code to me, which is by the endgame how the major artificial intelligences achieve that), tip the scales in favor of organics. Control will give an organic mind control of the greatest synthetic weapon, serve as a guardian and peacekeeper against it in the future (at least in a best case scenario). Synthesis allows both to combine, and as a result, there is no longer just synthetic or just organic, but a total combination of both.
I assume that, based on Shepard's dialogue (admittedly to Conrad Verner of all people, BUT...) that, as a device that manipulates dark energy, the Crucible resonates with eezo in some fashion to reach out across the various relays to do this all at once, which makes it a far more efficient solution than the Reapers - it happens all at once, rather than the slow harvest of species' over the course of decades or even centuries, and it needs the Citadel because of how it's the most massive Mass Relay in existence (since it would have to be to allow the Reapers to have formerly used it as their gateway into this galaxy). The Catalyst IS the Catalyst because it is the program that allows this.
But what happens is that, with the creation of the Crucible, the creation of these three new options for the Catalyst, the variables change. Now there's a solution to the problem before the Catalyst that is not what it had previously designated the 'best' solution, and has a higher chance of success. But, as a limited computer program, it cannot choose on its own, which means it has to be Shepard to make that decision in the end, because Shepard has free will and indepentent thought.