For starters, it depends on what you’re supposed to be trusting science to do. If you’re trusting science to provide you with a collection of knowledge that is definitely true, then you’ve misplaced your trust. Because that’s not what science is. Science is simply a methodology for refining knowledge, on its best day, science will provide you with the best understanding that we have currently achieved on a particular topic, and no more than that.
Are you trusting science to be a pure discipline, motivated only by the search of the truth? Because it’s not that either. Science and academia just as infested with politics, and ideology, and perverse incentives, and corruption as any other human institution.
Are you trusting the knowledge provided by science to be particularly sophisticated? Because depending on the field it might not be that either. If you require science to be capable of making repeatable predictions, then there’s entire scientific fields that are not capable of that. Psychology for instance has failed to reliably predict anything other than some rather broad trends, by some standards the entire field would be considered pseudoscience.
In any case, the solution we came up with for dealing with this issue was democracy. I think the real question that’s being asked here is “why are technocratic policies often not popular?”, there’s lots of reasons you could postulate for any particular policy, but in all cases democracy is doing its job properly by acting as a safeguard against unpopular technocratic policies.