Anyway, is there a reason for the catalyst to tell lies?
It's a Reaper (see Extended Cut, and shoot the kid).
Why doesn't it want Shepard to pick destroy? Self-preservation, as EDI states. They'll do or say anything to stay alive.
With a little bit of "oh, but if you pick destroy, bad stuff happens". So some people believed him, and picked the other choices. Allowing the Reapers to live.
Why give him the choice at all? Like with any game, it gives us the choice to kill the final boss. He doesn't want to get destroyed, but they put it in. Otherwise, the game doesn't end.
Shepard's initial plan was to destroy the Reapers. So that was always going to be a choice at the end. Even when standing there with the kid, he knows Shepard wants to destroy the Reapers. So he tries to convince him that the other options are better. He makes destroy really bad for him (being a Reaper), while control and synthesis really good.
Based on the player reaction, this little trickery he pulled off worked. People switched from destroying Reapers, to controlling or merging with them. Hence the Reapers managed to live, and stopped Shepard from destroying them.
Even though they put the option on the table to destroy, after his speech, some people didn't want to destroy the Reapers. They chose control, or synthesis. Or refuse, if they had the Extended Cut. They were convinced that the other options were better, and they made the choice to not destroy, willingly.
Another guy from years ago talking about the ending said it better than me:
1. On the Citadel, standing before the Catalyst, Shepard has the potential to wipe out the Reapers, an unknown race that has been around for literally eons. Any intelligent villain knows trickery will work much better than brute force when they have a gun to their head. What I mean is the options presented to Shepard besides destroying the Reapers seem like they could be last ditch efforts by the Catalyst/Reapers to save themselves. They have been around for millions of years. Do you really think they are going to beg and grovel Shepard, a mere human being who managed to out-wit them, or simply cast aside their pride to admit defeat? Of course not.
2. It's interesting to see how destroying the Reapers are presented as the red-Renegade option, whereas controlling them is presented as the blue-Paragon choice. Did BioWare do this or did the Catalyst? Once again, the Reapers are about to face their own destruction. How do you think their creator, the Catalyst, is going to spin this set of choices given the Reapers have been doing his will for an unfathomable amount of time?