Help me understand electricity - is the neutral always dangerous?
The water pressure/flow analogy is, unfortunately, a common but very imperfect one. If we insist on using it, voltage is something like pressure and current is something like flow rate.

The key concept you're missing is that you need a circuit, not a single wire.

Voltage, like pressure in the pipe, is always measured relative to some reference point. If you were perfectly insulated otherwise, you could hold the hot wire all day and not do yourself any harm, as birds on high-tension wires demonstrate on a regular basis. In the electrical analogy, this is like a capped pipe, or a connection into a tank where the outside pressure is the same as that coming from the pipe. You can extend that pipe or enlarge the tank, but as long as the counter-pressure from the cap or surroundings equals the pressure coming in, no current flows. (I'm oversimplifying like mad, but that's inherent in the faulty model.)

Only when there's somewhere for the water, or electrons, to go will you get current. In a properly designed circuit, that's the neutral, which in the water analogy we can almost think of almost as a drain pipe. If we were talking about DC, you could think of the return/neutral path as a drain pipe; to make that idea work with AC we have to remember that the whole system is sealed, current flows both direction, and we get our current from water sloshing back and forth in the loop of pipes rather than any one drop of water flowing all the way around the loop.

It's current, not voltage, that does the actual work. But voltage ("pressure") is what causes current to flow.

(Of course if you poke a hole in the pipe and let current flow in another direction -- not just stopping at you but through you to a ground, for example -- the voltage will happily do its "work" on you, which is why it's dangerous. Ditto for short circuits, where the "work" goes into heating up the wire and potentially starting a fire.)

Your electric meter measures the current, not voltage. Until the circuit is complete and there's a path from hot to neutral (or, in the bad case, to ground), no current flows and the meter just sits there. When current is flowing, the meter uses a bit of the energy from that current to advance itself; a gentle current spins the meter slowly, a strong current spins it more quickly. In an AC system, the meter is set up to measure both directions of the "sloshing", or to act like a ratchet so it ignores one direction, and again you get a measurement proportional to how much current is being used.

As I keep grumbling, this analogy really is not a very good one, because it leads to misunderstandings like yours. I've forced it a bit farther to answer your questions... but really, the best answer is to stop thinking of electricity by analogy and start thinking of it as its own thing, and just learn how it behaves.