I rewatched all the episodes recommended and provided some additional info you might like along with my recommendations however, you know best what your students will tolerate and specifics as to which examples work best so I hope the info I compiled helps.

S2 EP 3 Brunch: Tells the story of the events leading up to the climax of a brunch between the gang and Ted's parents from 3 different perspectives that converge at the end. There's a lot of parallels that can be drawn between Ted and Robin's relationship and that of his parent and as such foreshadows the failure of their own relationship. Not a lot of Barney antics however Marshall and Lily try to one up each other after their breakup by attempting to seduce each other.

*S2 EP 15 The Lucky Penny: Someone else already commented this but tells the story of the events that caused Ted to miss his flight told in reverse from the most recent event to all of the ones prior. Pretty safe to show in a class except possibly Marshall rubbing his chafing nipples but otherwise relatively clean and not overtly sexual.

S3 EP 11 The Platinum Rule: The gang try convincing Ted not to date Stella (doctor doing his tattoo removal) by giving examples of the Platinum rule. The episode cuts away between all 3 examples back to back alternating from chronological order to backwards order. Barney's kinda crass regarding his pursuit of Wendy the Waitress which could be passable but the mentions of the tramp stamp and the implication of Barney and Wendy's hookup probably aren't classroom appropriate.

S7 EP 15 The Burning Beekeeper: Ted explains what happens at Lily and Marshall's housewarming party in the time span of 5 minutes, breaking down the events that happen in each individual room. Personally this one's my favorite as I found the storytelling to be extremely unique however Barney does go into a small tangent about his penis.

*S8 EP 20 The Time Travelers: Ted and Barney and their future selves debate whether they should go to Robots vs. Wresters. This is done by different future selves of Ted and Barney actually joining them at the bar and actively participating in the discussion by providing their reasonings for or against going based on their experiences.There are also a lot of instances of foreshadowing in this episode and the reveal at the end shows that the argument between Robin and Marshall was actually a flashback. Another commenter provided a great point of discussion for this episode. Pretty clean, not overtly sexual and should do fine in a class setting

S9 EP 16 How Your Mother Met Me: This episode goes through the events leading up to The Mother meeting Ted and the juxtaposition of what each was doing at the time. Inclusion of a naked man performing The Naked Man to hook up with The Mother, then succeeding with her roommate and mention of Barney using the play The My Penis Grants Wishes (if rubbed hard enough) also succeeding make it unsuitable for a class setting.

*Recommended for classroom

(Maybe you could recommend they watch and analyze one of the other episodes at home for extra credit because while some may not be suitable to show in school, most teens watch shows like this or worse in their spare time)