A statement P about a single element in a dual or multiple set does not seem to

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A statement P about a single element in a dual or multiple set does not seem to logically exclude P applying equally to other elements in the set; yet we often talk as though "P is true of X" implies "P is not true of Y (or Z)", when X, Y, and Z all belong to some grouping. For example, take "Men work to support their families". Does this logically imply that women do not work to support their families? What about "African Americans suffer from discrimination"? Does this logically imply that Asian Americans, Hispanic Americans and white Americans (among other racial groupings) do not suffer from discrimination? Such objections are often raised in discourse. Given (x, y), "P is true of X" is thought to imply "P is not true of Y", or "Not-P is true of Y". If there is no logical exclusion above, what are these objections targeting? Is it a question of salience, rather than logic?