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I guess because democracy is about rule by the people. As soon as you start demanding training and/or qualifications you are drawing distinctions between the ruling and the ruled.
It's only relatively recently that we've established universal suffrage and property qualifications for voting, and given up the tendency for Prime Ministers to be from the Lords rather than the Commons.
Meanwhile, all our laws are still signed off by a family who have only just discovered they can marry outside of their own bloodline, and over 100 of our lawmakers are still in their positions because they've inherited a title or because they're senior figures in the Church.
Anything seen as a step back towards making politics more elitist and we'll probably have to give up our pretence at being a democracy altogether.
Finally, there's a tacit acceptance that politicians set the direction, and the real decision making and country-running is done by civil servants, who are experienced and well trained.
Question (not loaded): we demand expertise of the people who do everything from fix our plumbing to provide us with health care. People with training and experience. What is it about running the country which we feel doesn't demand any such training or knowledge? That you can pop out of your own work on sabbatical and still be a success at it?