I have been thinking about this question, for two reasons. The first is that I want to be able to quickly and clearly communicate to my students what the purpose of their philosophy class is The second is so that I do a better job designing the class in the first place.
Here is my answer to this question: teaching philosophy has two main purposes. The first is to teach critical thinking. The second is to teach a small number of substantive questions (and, if you're lucky, answers) from each text studied in the course.
Regarding critical thinking: I recently developed a sequence of questions for students to ask about a text, which will hopefully help them develop critical thinking skills, if they use this sequence for every text they encounter over the course of the semester.
Argument Analysis in 4 Steps
1. What is the thesis? (Is there more than one?)
2. What is the argument for each thesis? (Is there more than one?)
3. For each argument: Are the premises true?
4. For each argument: Is it valid (if deductive) or strong (if inductive)?
Regarding the second purpose of teaching philosophy: I need to work on this more, but my goal is that each text should have one or more substantive lessons for a student to retain and make use of later in life.
For example: Maybe Plato's Euthyphro teaches that moral truth is probably not based on God's will.
Maybe Descartes' Meditations teaches that one should be willing to question custom, authority, tradition, and the appearances of things, in order to discover the truth. And that many forms of dualism face the Interaction Problem.
Maybe Hume's Enquiry teaches that the logic of scientific discovery is not what people often take it to be. And that the argument from design has even deeper problems than those brought up by Darwin's theory of evolution by natural selection.
Oftentimes, though, I anticipate that the key lesson of a text will be an important question, rather than just an important answer.