I really like Wikipedia's opening line on science:
“Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.”
I also like the opening monologue from “Haloween on Military Street”:
“We measure things by what we are.
To the maggots in the cheese, the cheese is the universe.
To the worms in the corpse, the corpse is the cosmos.
How, then, can we be so cocksure about our our world?
Just because of our telescopes and microscopes and the splitting of the atom?!
Science is but an organized system of ignorance!
There are more things in Heaven and on Earth than are dreamt of in any philosophy.
What do we know about the beyond?
Do we know what's behind the beyond?
I'm afraid some of us hardly know what's beyond the behind”
Both, in their own way, do a good job of highlighting that our knowledge is fallible, and that at best we can hope to merely organize our understanding as it stands and find ways forward.
It would seem that claiming that science has a “monopoly on truth” is at odds with the admission that the grand sum of scientific knowledge stands upon the single caveat that it is based on observation, experimentation, and repeatability.
I agree that it would be the height of hubris to believe that we will or can understand everything in the universe, but it is not hubris to attempt the understanding of everything we have power to.
Whomever gave you the impression that humans are in any way infallible, weather following the scientific method or not, was a zealot.
Science is a way to organize knowledge. The scientific method is a way to observe, experiment, and theorize such that we can obtain theories that fit those observations and can be reproduced. Any other claims are either ancillary or false.