Why shouldn't two AC sources be connected in parallel?

Note: I am not trained in electrical safety. Do not rely on this post for safety advice. I know you are asking theoretically, but I feel like I should put this disclaimer here anyway.

Is it because the waves may not be synchronized and could then cancel out each other? Or something else?

That is the main reason, but the consequences are worse than just having the voltage cancel out.

Let's imagine the worst case where the sources are perfectly unsynchronized (180 degrees apart - opposite voltages all the time) and that the voltage is at the maximum when you make the connection. Remember that AC is just time-varying DC - at the instant when you connect them together, you have this circuit:

^{simulate this circuit – Schematic created using CircuitLab}

You've connected two voltage sources in a loop. Forget the load - what happens to the voltage sources? Well, V1 tries really really hard to make the voltage 240V, and V2 tries really really hard to make the voltage negative 240V. V1 makes lots of current flow from the bottom to the top, and V2 makes lots of current flow from the top to the bottom again. This is basically a short circuit, but short circuiting two sources at the same time.

If V1 and V2 are alkaline batteries, they might get quite warm. If they're NiCad batteries, they might get hot enough to melt plastic. If they're lithium rechargeable batteries, they will definitely burn up.

If V1 and V2 are inverters (as in double-conversion UPSes) the output circuit will probably blow up (literally).

If V1 and V2 are different phases of mains power, you'll get a big spark and pop the circuit breaker. If enough power is available, the spark (known as an arc flash) can be big enough to cause serious injuries. The main power feed to the datacenter probably can do that. I don't think you're likely to be seriously injured by plugging an IEC connector into a short circuit (even on two different voltage sources), but I still wouldn't try it.

If V1 and V2 are standby UPSes, running on the same phase of mains power, they should both be in phase - until one of them switches to battery power, at which time it will blow up because its inverter is now in parallel with the mains power.

When two DC sources are paralleled, blocking diodes prevent back feeding from one supply to the other. The supply with the highest voltage will always supply current without being affected by the other.

There is no comparably simple and effective provision for paralleling two AC supplies. Two AC supplies from the utility can be obtained with matching phases and voltages, but if one goes down, it must be disconnected to prevent back feeding. Even dealing with small voltage or phase differences is not particularly easy.

Danger to Wires

With this type of setup, while your intention may be that it would only ever be used with "one cable's worth of electricity", there is no guarantee. So someone could use the exact same configuration to get double power - e.g., 20A from circuit 1 and 20A from circuit 2 in order to have 40A total. There are a bunch of problems with this. In particular:

• Each of these two cables will have hot & neutral. In theory, the current on the neutrals and hots will be balanced - 1/2 the current on one wire in each pair. Actually there is no guarantee of that, but even if there is under normal circumstances, if one of the neutrals breaks due to a wiring problem somewhere, all of the hot - e.g., 40A in this example, will return on the other neutral. But neutral wires are not normally protected from overload in the US, so this would result in the wire handling twice its nominal capacity and potentially start a fire.

Danger to People

Normally, one circuit break is flipped to turn off power to a device. Let's say you have one of these 2 circuits also used for LED lights above the servers - just a few watts, so no big deal. Someone comes in to work on the light fixture. The servers are not on at the time. He starts work by turning off the breaker and verifying it is off and now has exposed wires from the fixture. You come in and turn on the server.

• The server can backfeed power from circuit 1 into circuit 2, which will now make the rest of circuit 2 - including the exposed wires on the light fixture hot and potentially fatal.