User blog comment:Markurion/How many of you put a bullet in Godchild in EC?/@comment-4672495-20120721205909/@comment-24174486-20120723180822

"Where in the ending, or anywhere throughout the series, do the geth (and not heretics) or EDI express a wish to eradicate all organic life, to give credence to the Catalyst's claim that this will inevitably happen?"

Short answer? They don't. Long answer? They do not. XD

The Catalyst believes that such conflict is inevitable and that the cycles prevent that from happen. It may very well believe that the geth and EDI don't want to wipe out organics... yet.

"for all we know, unions like that occured in almost every single cycle but the Catalyst kept ignoring them just like it did in the current cycle, or interfered and turned the synthetics hostile just like it did with the zha'til."

For all we know, synthetics in previous cycles did turn against organics. We don't have information on what happened in the cycles before the Protheans. All we can infer is that the creators of the Catalyst believed that such would happen—and even then, we aren't certain if the Catalyst's creators witnessed it happening or they were merely superstitious.