Then why can the Catalyst not choose, or change?
Because despite all his complexity, when you get to the core of what he is, he's just a tool... software... a very advanced Clippy!
That's why he's called "the Catalyst", because he needs an outside force to initialise the change and he cannot do it on his own. He was designed to be used by organics and so that seems to have never changed. He's been waiting a very long time for organics to come up with a new solution to the Cycles and impliment them, using his program to carry out the change. Part of the reason he's likely housed himself in the Citadel (or he is the Citadel) is because as an extragalactic Mass Relay, it's probably got the biggest power source in the galaxy and would been needed to carry out the program. While the Crucible was not of his design, it's basically just a software patch for him and gave him some new parameters to work with (Ctrl-Alt-Del).
So no, I don't think the Catalyst has true free will. He strikes me as just a program that's been stuck on "Continue Cycle? Y/N" for the last couple billion years.
(Of course, even if the people had figured out both the function of the Citadel, the Catalyst and designed their own Crucible, he kind of screwed them over by having the Reapers take the Citadel as the first thing they did in every previous Cycle. While it makes sense to protect himself since he must survive into the next Cycle, it still lowers the odds that any solution would be found. Frankly, the Leviathan was probably right when it called the Catalyst a "fundamentally flawed" creation since the Catalyst seems unaware he's stacking the board against the players every time and then blaming them for losing the game).