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Let's rewrite your deduction, in hopes that we will come to communicate. ;)

The system to which I refer is a result of evolution, not personal preference.
The rules describe the invariable bias of humans in favor of self-preservation.
The rules are encoded in our DNA.
The behavior of American soldiers is inconsistent with those rules.
The behavior of American soldiers is irrational.

It's that simple. We die for our causes, they die for theirs. If that makes them irrational, we are necessarily equally irrational. And if we are rational in sacrificing our lives for a greater cause, so too are they - surely you recall from your introductory logic that the validity of the argument is a formal matter, independent of the particulars.

Your notion that radical Islam sees death as an end unto itself is simply not supported by the evidence - if that were the case, why is it not extinct? They've certainly had 1400 years to achieve that goal, and yet they exist. For them, death in the service of a noble cause brings greater rewards in another life after death - I suppose I will only attract more scorn for pointing out that we preach the same thing in pulpits across the land every Sunday.

Your hatred and fear of them blinds you to their true nature. This is - dare I say - not a rational position to assume. I do not hate them, and I do not fear them - they are merely another danger in an endless series of dangers that must be dealt with. And the only way to properly solve this problem is to understand them for what they are, not by making them into cartoonish lunatics, unbound by any sense of reason.

They can be perfectly rational - or at least as rational as we are - and yet be completely immoral in what they do, just as we can be moral in performing acts that are logically indistinguishable from theirs. This is because motive is completely irrelevant to the rationality of an action, and yet entirely relevant to the morality of an action.

And if that still doesn't persuade you, ask yourself this - why is it that I am the only one here who has a reasonable basis to call them evil? Everyone else seems to be operating under the assumption that they are deluded or disconnected from reality or somehow otherwise mentally defective, apparently in preparation for sentencing them to a few semesters of logic and ethics. I find that...troubling, especially insofar as it provides a wonderful rationale for absolving them of their bad acts. No, thank you - they know exactly what they are doing, they know exactly what they want, and they act deliberately and with great consideration to further their goals. They cannot be excused by labeling them as "deluded" - such flies in the face of any sort of objective justice and morality we might imagine.

No, thank you. I cannot support this labeling of them as "irrational", both as a matter of practical reality and as a matter of principle. They are not irrational - they are evil. Period.