@blatham,
Well actually the chief Medieval religious thinker, Thomas Aquinas, acknowledged that what he called as the argument from authority (he didn't use the word proof ) was persuasive, but less than a real proof. After all authorities have been proven wrong before (and even back then, wise men knew that.)
In response to your interrogation;
1. I don't l know of any reliable a priori qualification standard for effectively holding that office. Looking back on our history there's a great variety of individual contemporaneous estimates of the qualifications of the candidates, Some (such as for Lincoln) were proven dead wrong in practice. Other candidates, looking back, were much overrated (Wilson was a disaster, despite his august academic credentials). Overall the available predictions were reasonably accurate, but there were indeed major misestimates. Still there is no absolute standard: we have a specific set of choices in this election, and a relative judgment must be made. I believe that if elected Donald Trump may well do much better for the country now than would Hillary Clinton. I also believe Hillary has as many significantly adverse factors ( evasion of responsibility & accountability, deceit, corruption in office)) as does Trump.
2. I see broad rejections by self-appointed spokesmen out there for both contenders. By what standard (or prejudice) do you choose among them? I'm not a perfectly consistent doctrinaire Conservative (or anything else for that matter) and am not generally swayed by such prejudgments, recognizing, as I do, that in this election we must make relative judgments about the effectiveness of the contenders in the specific conditions facing the country now, and the challenges that appear likely in the near future. It's situational and relative judgment, not an absolute one. Finally I suspect I am less respectful and more skeptical of the judgments of pundits, newspapers, organized political action groups and things like that than you appear to be.
3. I've heard arguments frrom some against Trump that I believe have merit: and others which I discount or even reject. However. I have not read all of the arguments of all of the newspaper editors and others who have announced their view that Trump is "unqualified" and frankly suspect the overereach that such preemptive judgments imply -- a bit pretentious and self-important, I think.
I fear these are not the compact answers you seek (or is it demand). However they are as complete and truthful as I can make them. I hope you will recognize that.
There is significant internal dissent and division in the Republican Party now, and a lack of any single clear leader. In contrast the Democrat Party has been living with a single designated heir for several years, It's certainly true that as the needed , polite opponent Bernie Sanders ignited some dissenting fires that were not easily put out, but it was done. The contrast between the respective party situations now is indeed stark: both are a bit abnormal, but neither is fatal. Reagan also faced serious dissent and resistence among Republicans but he achieved remarkable unity in office.