The text and the reader interact. Unfortunate interpretations of Louise Rosenblatt's theory of reader response have led some teachers to abandon the practice of close reading. What is unfortunate about this loss is that student responses, however heart-felt, which are based upon casual or inaccurate readings are often inaccurate and lead the reader into confusion rather than to understanding. Only then will they develop the skills they need to be powerful readers. Without it, as the chief instrument of Practical Criticism, reader response is merely personal, merely psychological, merely opinion.
Close reading is entailed in critical reading.
The kind of close reading that Berthoff describes does not come naturally to teenagers. Most prefer a broad brush stroke when explaining what they think about what they have read rather to a fine line of reasoning. The challenge for the teacher is to help students refine how they examine a piece of literature without destroying their confidence as readers. I start with students' responses but then ask prodding questions that encourage students to return to the text for answers. You say you hate the way Odysseus lies to everyone he meets when he returns to Ithaca.