Why was there a "point of no return" in the Chernobyl series that ended in the meltdown?

Through incompetence and ignoring operating guidelines they had maneuvered the reactor into a very unstable state, where small changes would result in large swings in power. They had:

• Run the reactor longer than expected in the run up to the test, resulting in a large amount of xenon, which "poisoned" the reactor suppressing the power;
• Disabled various automated safety systems, and cooling systems;
• Overshot the start conditions for their test, almost shutting down the reactor entirely. As a result they had to remove far more control rods than were recommended for safe operations in order to increase the power to the point where they could run their test.

They had put the reactor in a very low power state, but had removed all controls on positive reactivity. The xenon poisoning is slowly burned off over time, particularly as power slowly increases.

[Please note from this point there are various scenarios hypothesized in reports and articles about the accident. It's not entirely known why the operators used the AZ-5 switch. This answer is based on the scenario dramatized in the TV show that a runaway power excursion forced them into using it as intended as an 'emergency stop' on the reactor. ]

So, as shown in the dramatization, they suddenly find themselves in a situation where the power is starting to rapidly increase. The xenon is all but removed, there are almost no control rods, and to make matters worse, boiling of the cooling water makes the reactor even more powerful.

They see the power double every few seconds, quickly exceeding the maximum operating power of the reactor. They are facing a meltdown of the core. What do they do?

• Manually restore the full flow of cooling water and lowering the rods they manually removed? It's probably too late for this. The power is continuing to climb, and it's already far above where it should be.

OR

• Use the AZ-5 (SCRAM) system, which automatically lowers all the control rods, including those which they manually removed. Yes, this takes 16-20 seconds, but it does lower all the rods and it's what they are trained to do when things get out of control.

To me this does feel like they had already gone beyond the point of return when the power spiked. They were already going to experience a meltdown. The AZ-5 system just made it worse, because the graphite tips of the control rods just created localized spots of even higher reactivity, leading to the steam them hydrogen explosion.

Even manually lowering individual rods has the graphite tip problem. The spike in power around the tip as it lowered caused the rods to jam in position. The crew would not have appreciated this, but that route would have probably failed for the same reason as the AZ-5 system did. However in any case, they would have been trained to press the AZ-5 switch in these situations because it is the "emergency stop" of a reactor.

The AZ-5 button is the regular, non-emergency off button for that reactor, and they were supposed to turn the reactor off anyway.

The currently accepted answer presents some parts as facts which according to Wikipedia are not known to be true. It is not known whether the two engineers in charge knew about the impeding catastrophe when they pressed the AZ-5 button. There are several possibilities:

• Maybe they saw a dangerous power spike and tried an emergency shut down using the normal way they were trained to use.
• Maybe they didn't know about the dangerous power spike, but it did happen already, and they just tried to shut down the reactor for planned maintenance.
• Maybe no dangerous power spike had happened before they pressed the button and the movement of the control rods is what triggered the catastrophic power spike. This is possible because lowering the control rods actually increases reactivity in the bottom of the reactor first before lowering it many seconds later, plus the movement of the rods could have caused cavitation (spontaneous formation of steam bubbles in liquid water) in the dangerously hot water, further increasing reactivity.

The only power spike that is presented as a fact on Wikipedia is the power spike that happened after the AZ-5 button was pressed.

I mean surely they could not push the reactor to the "point of no return" to begin with, but once they got there could they revert their way back? Hypothetically if I traveled back in time to just before the AZ-5 button was pressed, at what step would there be a 0% chance of reverting it?

Again based on the Wikipedia article: The reactor had various automatic safety measures. All of them were turned off. The reactor was under full manual control. The reactor wouldn't reach a point of no return under normal operation, but it did because they were trying to run a test to determine what would happen under some emergency conditions and so they had to intentionally generate those emergency conditions.

The test protocol was worked out by the designers of the reactor and would have probably worked - except that the people carrying out the test went completely off-script, put the reactor into a non-design condition and then went on to do a modified version of the test which wasn't approved by anyone qualified to approve something like that.

Regarding the specific point of no return, that is impossible to know, but it could have been when they intentionally shut off the power supply for the water cooling system. Or maybe the point of no return was only after they pressed the shut down button, and the accident could have still been prevented if they had let the water cooling system work for a moment after turning it back on (it was only supposed to start working at it's normal power level again at the precise moment they hit the shut down button, so couldn't have dissipated the extra heat accumulated while it was not working properly), lowered the rods one by one (thus causing a smaller power spike for each one instead of a single large one) and only used the shutdown button once the reactor was once again in a normal state.

Disclaimer: I didn't watch the show, I'm answering only based on the real facts as presented by Wikipedia.

RBMK reactors use graphite tipped rods, which exacerbate fission upon installation. Light water functions as a coolant, while moderation is mainly carried out by graphite. Light water reactors in the US use water both as coolant and moderator; it's more expensive.......but safer. This means that the reactor's reactivity (adjustable by appropriate neutron-absorbing rods) has to account for the neutrons absorbed by light water. Water loses all neutron moderation as steam, with no water back systems (having been shutoff) the reactor went into overdrive.