So far, we have a mixed bag of answers but the question never really answered.

The question was (is): Why is it frowned upon (by some) to have a mirror on ones bicycle?

Some make it sound like if one uses a mirror, that person is less skilled or not aware of their surroundings.

I don't beleive that to be the case if a mirror is used. It's seems like a good extra tool to use, if needed. Just as in driving a motorcycle or a car, a good driver uses the mirrors regularly to be aware of the surrounding while still seeing the road ahead, without having to turn around. By the way, I do not have a mirror on my bicycle.