As Thomas Kuhn pointed out in his classic work, The Nature of Scientific Revolutions, Science as such is more concerned with confirming already established theories, or paradigm, than with facing new evidence. Such evidence - anomalies - is swept under the carpet, and the new theories or paradigm explaining it rejected, until a new generation of scientists come along who are willing to accept the new position. The result is a "scientific revolution", and the establishment of a new paradigm. Thus, to give some classic examples, the heliocentric (sun-centred) cosmology of Copernicus was only accepted over the old Ptolemaic geocentric (earth-centred) model of the universe after much resistence, although the celebrated trial of Galileo, who supported the Copernican theory, by the Church, was more a matter of personal politics. Another, more recent, example: the "new physics" of Plank, Einstein, Bohr, de Brolgie, Shroedinger, and others, became a new paradigm that replaced, with rather greater ease, the old Newtonian physics.
An example could also be given of a "paradigm that failed". In the late sixties and early seventies it really seemed as if the data of parapsychology, so painstakingly accumulated by J. B. Rhine and his successors, would soon be assimilated into mainstream scientific thinking. For Psi- phenomena are no more strange - and often a great deal less so! - than some of the wierd and wonderful implications of Quantum Physics . But such was not to be, and parapsychology soon reverted back to the reviled status of "psuedoscience".
The trouble with paraspychology is that, though harmless enough in itself, it would have very quickly lead to other far more threatening things, like occult and psychic phenomena and realities. Thus it was unacceptable for all reasons.
So, it is not that science is irrational. Science is rational; within the compass of the paradigm of the day. But once it moves beyond those limits, it becomes an irrational dogma, Scientism .