Electricity and fire on a good day

But you explained to him that this is not a correct comparison, so why are you encouraging him to light it?
By the way, if electricity is lighting a fire, then why is it permissible to turn on electric pressure pumps when you open water taps in the house? The pressure in the tap is an indirect reflection of an electric pump.
Is it permissible for me to put a temperature sensor and set the air conditioner so that when it reaches temperature X (the environment), the air conditioner will turn on automatically.

Pumps are not allowed to be operated. Although if it is a device or mechanism that operates them at fixed times, there should be some leniency.

The Rabbi said:
“Regarding lighting a fire, the Mishnah Bitza 33b prohibits it. And the commentators are divided on the matter (see Rambam and Rabbad 4:4, 50). Some attribute this to the prohibition of giving birth (according to the Rabbad, and to Rabbad it is because there is no preparation here), and others (Rambam and Rashba Beit Moed Shab 2:6, 7) in that what is possible from the day before is prohibited on the day. Some understood Rambam to mean that the prohibition is due to the hassle involved in lighting it, and therefore permitted matches and an electric bulb, which are not a hassle. But this is urgent and was rejected by the poskim.”

If the Toli initially attributed the prohibition to the hassle, they should also have prohibited the hassle of preparing food on Yom Kippur - isn't that so?

And I wanted to ask about the hassle involved in leaving the ”candle”=”fire” lit all night (getting up and checking) to add oil or wood to the fire. Isn't that a hassle?

They didn't even forbid complete soul-destroying deeds, so why should a nuisance be forbidden?
And in general, there is no such thing as a nuisance. What the sages forbade is forbidden, and what is not is not.

It's quite interesting because usually only the men would go on pilgrimage. Remember, who would cook for them there? The women were at home. So if they were busy with food all day long, how would they feel about the holiday? This is where the idea of the hassle of preparing food came from. After all, nowadays you buy a lot of ready-made and canned food that is easy to cook from. But in their time, everything was done by hand - there were no refrigerators and no canned food in boxes.

To the questioner: I am not a rabbi or adjudicator. But many good people have already permitted it, from Rabbi Raphael Aharon ben Shimon of Egypt, Rabbi Yosef Meshash, Rabbi Zvi Pesach Frank, Aruch Hashulchan, Rabbi Uziel, Rabbi David Shlush wrote a long reply on this with all the aspects and concluded that it is permitted.
The extinguishing is in dispute.

The Rabbi wrote elsewhere that the prohibition of electricity on Yom Tov is because of a molid, while Rabbi Uziel generally claims that a molid is not a prohibition, what is the Rabbi's opinion on the subject of a molid?
https://haravuziel.org.il/%d7%a1%d7%99%d7%9e%d7%9f-%d7%99%d7%98-%d7%90%d7%95%d7%97/

I estimate that there is also controversy about this molid…

After that, my opinion was inclined that it is forbidden because of a builder. There is a long column here about it. As for Molid, these are ancient things.

Rabbi:
I also once thought that electricity was the transfer of fire and not the ignition of fire. But I think that is incorrect. I am not sure that this is a misunderstanding. This is a question of reasoning, not of physics.

What is Rabbi's reasoning?