You might want to read my response carefully. You misunderstood or inaccurately assumed a few times.
Additionally I should point out: Science cannot answer "Why" questions. Science is descriptive and thus it will answer any of the other Ws (Who, What, When, Where & How) but it will not give normative conclusions based on descriptive data. You will need another source to answer the "Why" questions be that Religion or another Philosophy like Humanism.
Why does a heated pot boil?
Why is the sky blue?
Why does me pressing buttons make words pop up on the screen?
If only science could answer 'Why' questions!!!!! 
As you where actually talking about silly philosophical [<<*key word alert*] questions like "Why are we here?", that presupposes that there IS a reason we are here. It is a question that states we are here to cause something and not just here as the effect of something. Why do we feel the need to have a purpose? (the SCIENCE of psychology might help you with that one...philosophy, not likely)
Actually, Scientists (including myself) cannot tell you why heated things boil. They can tell you how they boil in this reality where they do boil. However they cannot tell you why heated things do not freeze instead. They cannot tell you why this reality exists rather than the reality where boiling something will freeze it.
So scientists can tell you that, in this universe, the path of light passing from space into the earth's atmosphere results in our eyes perceiving it as blue. We could have evolved to see the sky as orange. Scientists cannot tell you why we do not perceive the sky as orange but they can tell us how we see it as blue.
An electrical engineer could tell you how the buttons you pressed resulted in the letters on the screen. A psychologist could tell you how people decided to construct the machine that way. However neither can answer why this future instead of an equally plausible future where computers don't exist.
Now if you ask a philosopher they will be varied in their answers including the possible answer of "This reality was random and has no deeper meaning."
However I suspect part of your objection is due to a semantic misunderstanding. Please look up the term Normative Claim relative to the word Descriptive Claim. The word "Why" usually fits the pattern however English is a twisted language.
Sidenote: I was not talking about silly naive questions like "Why are we here?". Philosophy is quite sophisticated with its questions. Try: "Why be moral?" aka Why live in accord with moral truth? Moral Truth is defined below. This question is closer to questioning the assumption than it is assuming the assumption.
Is it irrational to rely on Faith where evidence cannot exist? Do you reject the hypothesis that murder is immoral simply because you do not have enough evidence to reject the null hypothesis that it is morally permissible?
It is contradictory to hold the position of requiring evidence except where evidence cannot exist?
Murder being immoral is a societal standard not fact, these are HUGELY different things. Morality is fluid, Facts are not [they can be wrong when science derps here and there, but we fix that in time (YAY FLAT WORLDS!)]. In some cultures you murder your way to the top of the tribe, once there you are revered as a god for your cunning and ability to survive. For them, murder is a good thing, as a way of culling the weak...like every other "uncivilized" creature on the planet. I have murdered a deer, and it was super yummy...nobody tossed me in jail. I know some wonderful folks that murdered a fairly large number of people between them...then they came back home, hung their uniforms up, and went back to school on the GI Bill, nobody locked them up, in fact, they are regarded as heroes.
Now, on to where your argument could actually hold. Can one reject that aliens/a wizard god/etc exist because there is no evidence at all? Nope, one can not outright reject those and call themselves scientifically minded. I trust that was actually the point you where making.
I accept that there are a LOT of holes in what we 'know to be true' about our silly stone spaceship, but science tries to fill those holes and actively peruses answers. Religion simply does not. To have faith, to accept something without evidence of any kind as truth, strikes me as unproductive and lazy. Having faith, and the peace it brings you [ignorance IS bliss, and i mean that in the least offensive way possible], is what some people still need to get through the day. It makes them feel better, it helps them not worry as much about the rigors of a fairly grueling and harsh world...same goes for people that smoke WAY too much pot...
I am 100% on the science side of this argument every time, but I in NO way discount the possibility of something more out there that we simply have not discovered yet...It could very well have been handed to us in a handy book...but, prove that is is all you say it is...until then, it is a popular book full of quaint stories that has been interpreted and translated by the less-than-infallible hand of man.
On the proof/disprove god thing...You can not disprove the existence of something. I have the ability to set things on fire with my mind...now, without requiring proof that this statement is in fact true, disprove it. There is a wizard named Sam that lives in a yurt on an elephant's back somewhere in the depths of space, that created our galaxy from bits of laughter and a dash of garlic. That sounds exactly as absurd as an all-powerful entity creating life from nothing, then refusing to prove he/she/it exists...but, prove that Sam is not real. The burden of proof lies with the religious folks at the moment...You have your hypothesis "God exists [etc]", on to step two.
1) Important vocabulary:
Moral Judgement: Assertions about Moral Truth. [Fluid]
Moral Truth: Truth by which statements called Moral Judgement are either True or False. [Static]
Now with that vocabulary lets examine my argument:
1) Evidence that would let one know the Moral Truth relative to a Moral Judgement is
impossible in favor or in opposition to the Moral Judgement.
2) There is a Moral Judgement that "Murder is Immoral".
3) There is no evidence for or against this Normative Claim.
4) Would you reject Normative Claims that lack evidence in the same manner you would reject Descriptive Claims that lack evidence? (aka would you assume Murder was not Immoral due to lack of evidence that it was Immoral?)
5) Is it contradictory to reject Descriptive Claims that lack evidence but not necessarily reject Normative Claims that lack evidence?
What am I NOT claiming:
Descriptive claims do not need evidence.
Scientists should believe any and all claims that cannot have evidence.
Scientists should believe any and all claims about things that could be tested in the future.
Lack of proof is proof of lack.
What I am claiming:
Rational belief in provable claims requires evidence. Lack of evidence for a provable claim is evidence that the claim might be false. This evidence supports the Null hypothesis rendering the Null superior to unproven provable claims.
It is not irrational to believe or disbelieve unprovable claims. The lack of evidence for an unprovable claim is not evidence that the claim is false. Therefore there is no evidence that supports the Null hypothesis either. Since both have no evidence then neither is superior.
It is not irrational to require evidence for provable claims but not require evidence for some unprovable claims.
Some forms of Religion are not irrational.
