The concern with falsifiability with regards to science rigor gained attention by way of philosopher of science Karl Popper's scientific epistemology "falsificationism".
Popper stresses the problem of demarcation—distinguishing the scientific from the unscientific—
and makes falsifiability the demarcation criterion,
such that what is unfalsifiable is classified as unscientific,
and the practice of declaring an unfalsifiable theory to be scientifically true is pseudoscience.
This is often epitomized in Wolfgang Pauli famously saying, of an argument that fails to be scientific because it cannot be falsified by experiment,
"it is not only not right, it is not even wrong!"