I note that one can quote someone they disagree with in order to establish a point of contention. This means the question is a false dilemma as one can choose to quote somone they do not admire and do not agree with. To quote no one in particular "A false choice is worse than no choice at all".
When I quote a person it is because the point they are proving or stating is something that I agree on because if I don't fully agree on the thing they are quoting it's not like you should take part of the quote out and I don't know really anyone that would remove part of the quote because if you remove it, then your really not quoting them. I think that if you quote someone you should agree with the quote and not just adire a biased point
When I quote someone, it's normally because I happen to agree with the quote. In some cases, it's even when the quote has come from someone I despise on an ideological level. After all, even a stopped analog clock can be right twice a day. You just have to find humor and wisdom where you can.
I would only quote a person if I completely or mostly agreed with a quote. I would not quote a person that I admire saying a thing that I don't admire. I will even quote someone I don't admire if I agree strongly with their words, as long as they aren't a terrible person.
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Awful people say brilliant things sometimes, and brilliant people make a mistake or say dumb things with equal frequency - nobody is right or wrong all the time. A quote is a simple example of something that everyone can understand and that speaks to people - the person is not the point.