In a conflict, is it better to explain yourself or stay silent?

Sometimes we try to explain ourselves to the other person only to find out that they have already made up their mind about the situation.
I think that most people these days have learned not to over explain things to the other person - because it doesn't seem to matter what you say, they're going to believe what they want. Period.
In a conflict, is it better to explain yourself or stay silent?
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