>Higher interest rates curb all economic activity, both supply and demand.

But not equally, which is the vital missing link here.

Activities that are currently highly profitable will continue and possibly even grow, despite the higher interest rates.

However, activities which are unprofitable, or who have a long horizon to their ROI break even point will be affected, and will shrink.

That's the whole point. We don't want to curb EVERYTYHING, and we won't. We will leave the important, valuable, today stuff going... but we will lose the less important, less valuable and/or tomorrow stuff.