If the Star Child is a sinister being, why give Shepard control over its fate? Clearly it doesn't because Shepard's response to controlling his own fate is to kill everyone.
We kind of glossed over this during the conversation but here's what I took away regarding why the Catalyst even interacts with Shepard:
The Catalyst says that its solution won't work anymore because Shepard's here standing before it.
The Refuse ending made what he meant here clearer to me.
It realizes that eventually its going to get beaten. It thought the Crucible design had been destroyed yet here it is parked at his doorstep. The Protheans managed to bungle up this cycle's harvest and here this cycle is, fighting the Reapers on a unified front. They might be doomed, but maybe if things had gone different the roles would be reversed and that's a possibility it can't ignore.
It knows now that whether its the next cycle (as is the case in Refuse) or a hundred cycles from now, it can't stop the transfer of information and knowledge that's already taken place and that the Reapers are eventually doomed. So something
else has to happen now which is why it brings in Shepard to confer with.
It doesn't like Destroy for obvious reasons which is why he down sells the option but at the very least in its view it kills all the Synthetics.
The Catalyst seems uncomfortable with Control (and in fact admits he doesn't like the idea of being replaced), but at the very least Shepard can use the Reapers should the need arise.
He still sells Synthesis as the best option (its the only one he actually argues for) since that's the one that completes his core programming. The other two options are in his view compromises. This is the one he wants.
Choosing Refuse sends it into a fit, the two of you are at an impasse. Since we know now that the Catalyst is the
collective Reaper intelligence + whatever portion of it is stored on the Citadel (which I imagine to be where the original Catalyst AI is housed) ala the Geth Consensus I would wager that whatever portion of the Reapers that are in favor of outright just completing the harvest (the Sovereigns of the Reapers if you will) as opposed to compromising win out - hence the outburst.