It's an oversimplified saying by Musk. Cars, buses, bicycles, trains, and pedestrians are all 3-dimensional "objects", however the issue is cars simply take up way too much public space. Having 1 person per 5 man car and having 90% of people use those 5-man cars is clearly a very sub-optimal solution. If we convert 50% of those drivers to other modes of transport, we'd see a LOT less congestion, without tunnels or flying cars or anything new.

It's easier to understand if you think about the tunnels as lanes. Each tunnel can still have busses and cars, but you can also stack them on top of each other. You can do that above ground too, but it looks super ugly and you can't really go 10 stories high. Underground you can.

He probably shouldn't have driven a Tesla through it, the only message people got was that the 1% are going to have tunnels. Really you'd run autonomous buses and 4 person taxis through it. Easy to imagine it being much cheaper than public transit too.

This sounds more likely, it's much easier to imagine 20 tunnels than 20 lanes of traffic (250 feet wide). And much pleasanter to have it all underground where you don't have to look at it.

Elon Musk isn't an expert on urban design, so why should we care that he has a simplistic quip about a really hard problem?

Informed people understand scale. Going from 2D to 3D is like going from O(n^2) to O(n^3). It's quite a big difference at scale. Going up in dimensionality is like going from one order of magnitude to another, only more so. (Actually, it often makes an additional two or more orders of magnitude accessible.)