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The usual discussion follows. People say "oh, yes!! So long as the father is not a wife beater, child molester, child neglector etc". But no one suggests that the mother could have any of these faults.
Everyone assumes that the mother is a good mother, except that she does not allow visitation. We ask her if the father is bad. She says "Oh yes! All of the above and more!"
Everyone says "Well he is a man, after all. Keep denying visitation, then."
Status quo, because fathers are assumed to be bad and mothers are assumed to be good.