There is no direct antonym for "minister", like there is for religious person which would be atheist, as even the Church of Satan has priests. The closest you could come is "non-minister" or layperson perhaps, but that is stretching.
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This word does not have an opposite.
The opposite of the word "answer" is "question."
The opposite of the word "constant" is "variable".
There are no opposite words for analyze. Also just saying the opposite of a word is called an antonym.
Different, dissimilar, unlike, change, or variable. Those words are opposite of same.