Students should think with this awareness in mind, with some sense of the limitations of their own, the text's, the teacher's, the subject's perspective. See perfections of thought. A sentence having two or more possible meanings. Sensitivity to ambiguity and vagueness in writing and speech is essential to good thinking. A continual effort to be clear and precise in language usage is fundamental to education.
Ambiguity is a problem more of sentences than of individual words.
Furthermore, not every sentence that can be construed in more than one way is problematic and deserving of analysis. It is a poor example for teaching genuine insight into critical thinking. A government that gives money to people who haven't earned it corrupts both the giver and the recipient. Evidence and considerations relevant to one interpretation may be irrelevant to others. All learning presupposes some analysis of what we are learning, if only by categorizing or labeling things in one way rather than another.