Let's examine the claim: Any valid explanation of the universe must be scientific.
This is an increasingly common argument, and is at the root of the evolution vs. creation debate. The proponents of darwinian evolution seem to think that all they need to do is point out that any account of creation is not scientific and thus can be dismissed out of hand. (There are those who try to dress up the creation account with science - but that's another matter). The root of the issue is, is it valid to say that there are not, nor have their ever been any miracluous/supernatural events and so everything in the universe can be explained by science alone?
It could obviously be pointed out that such a statement is intrinsicly atheistic, and so is at odds with the beliefs of many of the greatest scientists of all time: Newton, Maxwell, Einstein... but let's examine this statement with logic alone...
Let's assume for the moment that they are right. And that there is nothing supernatural - not now - not ever. This means that, as they claim, everything that happens must happen for a well defined scientific reason. It may be a reason that scientists do not yet understand, it may be for reasons that are so complicated that they cannot in practice be unravelled, but they are all natural, and within the remit of scientific investigation. Every physical effect has a physical cause and nothing outside of the universe itself is needed by way of an explanation. It sounds like athiestm... because it is - and it has become a very prevalent world view in modern science. But is it consistent?
If every physical effect has a physical cause, then those causes themselves must be effects of prior physical causes - as we are not permitted to entertain any other source of influence. We can think of all the events in the universe like chains of dominoes streching back in time. Each domino falls over because another domino topples into it - cause, effect, cause, effect. Although in practice dominoes may fall over without another domino, this would be caused by gravity and possibly floor vibrations and thus in our analogy would represent another well defined domino/cause. What we are not allowed now, nor at any point in the past, is a domino that falls over without a prior domino - as this would represent an effect without a cause - an event that is not explainable by science - a supernatural event.
Such a world view makes sense, if like Einstein, you believe that the Universe is eternally pre-existent. But no-one believes that any more - even Einstein was convinced by the evidence that the Universe had a beginning.
If the Universe had a beginning, then we run into problems with our domino chains - we can extrapolate them back further and further into the past and so defer the problem, but sooner or later we have to face the inevitable. There must have been a first domino! This is exactly what we have said cannot happen: a cause that does not depend on anything prior for its existence. Something that is outwith the remit of science!
So if believing that "everything can be explained by science" leads you inescapably to acknowledge that there is at least one event that cannot be explained by science then it proves that the original assumption is untenable. There are some things about the universe that cannot be explained by science. The Universe itself is proof of the supernatural.
Those who try to dismiss men of faith as irrational are themselves holding to an irrational worldview!