> Physical systems governed by classical mechanics are reversible just by perfectly inverting all forces, velocities, and rotations
This doesn't really make sense. To do that you'd have to end up bringing in quantum dynamics, and well... we know how that goes.
Heat is probably the best example, as even if you were able to track the movement of particles individually you'd have a very difficult time putting them back in order. The development of thermal stat-mech is one of the things that led to the quantum revolution and "new physics". But if you only have a "calculus" based understanding of physics you likely aren't going to be familiar with this. It's not much discussed (it is some) if you didn't start entering upper division physics classes or equivalent coursework. It really shows up when you get into the weeds, but understandably it isn't something stressed before then. Physics is hard enough...
Not all classical physics is time symmetric[0].
FWIW, I don't think the article is unclear. I mean they address your point in the first sentence of the second paragraph
> Intuitively, it feels like the only way to undo a complicated sequence of rotations is by painstakingly doing the exact opposite motions one by one.
[0] There are examples on this page that do not require relativity or quantum mechanics, even though some do.
https://en.wikipedia.org/wiki/T-symmetry[note]: The real paradigm shift in quantum mechanics was that there was information that we could not access. That's what Schrodinger's Cat is about. The cat doesn't sit inside a parallel universe, a quantum superposition. It is just that there is no way to know which of the states the cat is in without opening the box. It says that we cannot have infinite precision, therefore must use statistics. So Einstein's "god doesn't play dice" comment is about that there must be some way to pull back that curtain.