I honestly can't think of anything off the top of my head. There's plenty that I personally wouldn't indulge in, but just understanding why younger people like a particular trend isn't that hard. If anything, it's older people not understanding a particular trend that makes me baffled. Stuff like not understanding skibidi toilet (it's just gmod + body horror), not understanding Tiktok (if you can understand the appeal of dancing badgers with music being played in the background, you can understand the appeal of Tiktok), not understand streamers (if you can understand why people would football on TV or why people follow celebrity gossip, you can understand streamers). To go over your examples:

1. ASMR: It's just a particular genre of Youtube video. Genres can be quite specific. I personally like the genre of video where you watch a timelapse video of a plant growing from a seed. I think ASMR got popular because you don't have to actually watch the video since it's all audio. So, you can just treat the video like a podcast while doing chores or studying.

2. Instagram: It's just a social media site that grew large enough, and once a social media site is large enough, people will go to it no matter how much of a dumpster fire it is (see Facebook, Reddit, and LinkedIn). I mostly see Instagram as taking the photo part of Facebook and turning that into its own thing. There are people with 10000+ photos on Facebook, so why not create a social media site specifically catering to those people? We already have imageboards like 4chan, so the idea of a social media site centered on images is nothing new.

3. My students' taste in anime: I mean, Azumanga Daioh aired in Japan 5 years before they were born. Like, it predates Lucky Star and K-On. If you showed me those GI Joe cartoons from the 80s when I was a teenager, I would've given you a similar response. It's also an awkward time period where it's too old for me to enjoy as a kid but too new for my parents to enjoy when they're kids. If you showed me The Adams Family or some other boomer show when I was a teen, you would've at least gotten a "oh yeah, my parents showed me these before, and I thought they were pretty cool." There's a decent chance you would get a flash of familiarity if you showed them Transformers or GI Joe since their parents (or at least their dads) probably watched them.

4. Photo and videos done in portrait mode: It's just a stamp of authenticity and immediacy that translates to an aesthetic. Awhile back, there was a trend on Tiktok poking fun at how millennials start videos with this 5 second awkward pause while zoomers start videos by fumbling their phones. Even though they're very different on the surface, they're ultimately both trying to convey the idea that the video isn't edited but something that spontaneously happened. The millennial video has that 5 second pause to communicate that it was done unscripted with a single take, so I have to gather my thoughts for 5 seconds. The zoomer video has the fumble to communicate how I spontaneously wanted to create this video out of the blue. To loop back to portrait mode, if you take out your phone from your pocket, you're already holding it in portrait mode, so shooting the video in portrait mode is to communicate, "oh my God, I just have to shoot the video. I don't have time to flip the phone to portrait mode. I have to shoot it now." Eventually, it just becomes its own aesthetic just like how Unregistered HyperCam 2 became an aesthetic for certain early Youtube videos.