why are random selection and intelligent design mutually exclusive.
They're not, in principle; one could easily imagine a cosmos in which an intelligent designer imposes various levels of order on an underlying process that's undergoing random variation. Indeed, Plato's Timaeus describes such a cosmos—the Demiurge whips the pluripotent and randomly shaking Receptacle into shape using mathematics and the eternal Forms.
But the project of modern empirical science dispenses with final causes, intentions, in favor of lawful but impersonal energetic interactions. The evident successes of science bespeak the wisdom of this project.
You don't even have to imagine that universe. I have seen computer programs that "evolve" virtual creatures whose body plans and primitive locomotion looks just like that of the the creatures from the cambrian explosion.
That is while there is random selection there is not random results.
It just looks like the line about how many are called but few are chosen. Why? because few actually meet the criteria called for.
So what's the criteria. There are zillions of things that have to go just right from the macro the micro in order for creatures such as ourselves to even exist.
I'm not saying this particularly means anything.
But random selection seems to presume a disorder at bottom of things that breaks against the evidence of the eyes as severely as any promulgation that there is an ultimate invisible order.