Why the outrage over a Peloton and a Rolex?

This has been a question I've been thinking about and it brings me back to a discussion I had during a class. The professor stated that Peloton had been an innovation.
I disagreed, asking how a glorified exercise bike and a iPad was innovating.

This statement was much more controversial than I expected and immediately drew backlash from the other students. Judging by the number of $1000 coats; maybe 5 of the 20 students were not very wealthy. Comfortable; but not "rich."

The less intellectual argument was that I was out-of-touch because I could not afford one. If I were wealthy enough to own one, I would appreciate it for what it was.
The more nuanced argument that emerged was that it allowed for the gym experience, at home.

After a back-and-forth, wherein I still didn't "get" the appeal of a Peloton; one particularly insufferable student said what the others had danced around: [I] didn't "get it" because it was never meant for people like [me] to "get;" and the Professor agreed.

Owning one signifies a certain level of wealth. The innovation, such as it is; is that it allows people with that wealth to work out with one another remotely. It is a gated-community for exercise.
That's what the faux-outrage is about.

That's what the outrage of President Biden owning a Rolex is about as well (never mind that Presidents are gifted the watches by the manufacturers).
It punctures the notion of the virtual caste that the ultra-wealthy have isolated themselves in.

To them, he cannot call himself "working-class Joe from Scranton," because that exists outside of and debases the walled-garden.
Working-class people are simply not meant to possess these things.

In the class, my $10 Nalgene bottle signaled who I was. My $125 (On Sale!) N2B Snorkel Parka signaled who I was. My 3-for-$20 t-shirts were what I was meant to possess.
I didn't "get" why they would spend hundreds on one shirt; because I wasn't meant to "get it."

If President Biden is a "working class" guy; he isn't meant to possess the trappings of wealth in the eyes of the extremely wealthy. Those are luxuries meant for a few; not for a person of his proclaimed caste.

Post-Script: These were the adult children of multi-millionaires, who themselves never worked a day in their life, arguing with a guy that retired comfortably at 38 and will not want for the rest of his.