Hi Shalom,
Why teach Gemara at all? Without elaboration, the Gemara is Judaism. Without it, the Chumash can be interpreted as the Christians, Tzadukim and Karaites did. Additionally, the reasoning in the Gemara allows us to apply halacha to new situations and technologies, making it a "living Torah".
To teach Gemara in yeshivos is no question. The real challenge is teaching Gemara to populations which do not emphasize its study. When Gemara becomes just another course among many, and when it must compete with pop culture, it becomes a challenge for the teacher to motivate the students to parse through the idiomatic expressions and sometimes arcane situations.
If Gemara becomes a "Gemara appreciation course" for a population which will not be visiting the Bais Medrash regularly, then you have a good question; why then teach Gemara?
In truth, teaching Gemara shows the students that Jewish law comes from a sophisticated, peer-reviewed dialectic, where all ideas are held up to scrutiny in an intellectually honest atmosphere. They need to know that the halacha is not just "because the rabbi said". Additionally, studying Gemara should also give the students a sense of Mesorah, that they are part of a long, continuing chain. This broader view of their role in Jewish history should hopefully lead them to a greater sense of importance, strengthening their Jewish identity.
As I mentioned above, this is quite a challenge for a population not fully committed to the intensity of Gemara study. I personally do not dwell on the same Gemara the entire year, rather I search out and choose texts which both illustrate the dialectic and have some modern application which might be appealing to teenagers. (If anyone has a similar situation, I would be excited to hear suggestions of such sugios).
Sincerely,
Rabbi Jeff Holman
Jholman613@sbcglobal.net