You have to admit, accepting something unquestioningly, something for which there is no evidence and which offers no greater understanding of how the world around us works, does seem a bit irrational.
As for this universe coming from nothing or a "big bang", that is the best explanation science has come up with; but even if it isn't the whole story, contrary to religion, it allows us to make predictions and gain a deeper understanding. In short, it allows us to make more rational choices in relation to our environment. Religion on the other hand doesn't evolve, doesn't adapt to new knowledge.
"Religion" or on a more basic level, the belief in intelligent design gives me the basis in which to see that there is order and a design in which the world operates. To me a world without an intelligent designer would be as irrational as having a computer operate without any software. The computer could perhaps have "evolved" from nothing and just be a chunk of metal, but there had to be an intelligent creator of the software that gives the program the design it needs to operate. Even changing one piece of code, or taking code out causes the program to fail (kind of like what happens when there is an "error" in our DNA code which causes problems in our bodies with mutations and so on.)
The fact that we have DNA shows that there was some planning or "information" that took place to begin with. In a way, information in our world and in our structure proves intelligence and a "designer." So it is logical to think that there was a plan. Without that the world might exist but we would not have intelligence at all.
The order you see is already mostly explained by the laws of physics; simply adding a god to it doesn't help in any way, shape or form, we gain no new understanding, and it limits the questions we can ask about the world, because the answer is an arbitrary "god willed it so".
And what you go on to describe, it basically comes down to the old "Watchmaker analogy", which hasn't been seriously considered ever since the mechanisms for evolution of species were discovered; in no way does it follow that the existence of DNA proves there had to be a designer.
