I suppose the most straightforward and general answer to this is: understanding is a process, and alchemy is from a much earlier stage of that process than chemistry and electricity.

more importantly, why is wood not in the four western elements? Wood fucking rules

Because ancient people are dumb.

In Avatar: The Last Airbender, Lightning is part of Firebending.

In Chinese culture its actually: 金木水火土

There is apparantly 5 elements. And Metal (金) and Earth (土) are separate elements. In this universe Toph Beifong is not an Earthbender, but can only do Metalbending. Lolol.

There should be a 电 （Electricity）

Funny how Air isn't even in the Chinese version of the elements, so:

金木水火土电 and 气

Metal Wood Water Fire Earth Electricity Air

7 Elements to conquer the world?

Might as well just pull up the periodic table lmao.

The Greeks knew of electricity, knew of static shocks and lightning, but since the only thimgs they could apprise of it was that it zapped you and made noises, they must have assumed that it was something secret.

Zeus's lightning bolts must have been hammered together of billions of those tiny zaps you get from sheepskin and amber. The blacksmith that can weld lightning must be a deity, all in all it is too great a subject for mere mortals.

And then Ben Franklin came along and slew Zeus and stole his lightning.

Mostly because the only real exposure to electricity the people who came up with the "classical" elements had was lightning. I'm sure they experienced static electricity from time to time, but they probably didn't associate it with lightning.

From their perspective, lightning is a very brief moment of extreme light, then maybe a fire if they can actually see the impact site. So it seems a lot more closely related to fire than we would suppose.

maybe there is a scientific explanation of why it isn’t

Nothing about the "classical elements" is rooted in what we would understand as science today. It was just people making guesses about how the world around them worked without the rigor of the scientific process. It was little more than wild speculation.

Maybe they just didnt know what electricity was. Maybe it was lumped in with air and/or fire.

Give me alchemy, give me wizardry

Give me sorcery, thermatology

Electricity, magic if you please

Master all of these, bring him to his knees

I master five magics

-- Megadeth, Five Magics

Because electricity isn’t an element, it’s fairies. That’s why when there’s a short you see smoke: it’s really the fairies escaping the wires.

It’s a combination of fire and air, possibly just fire

not sure what stories and fantasies you like reading, but most elemental magic systems i know of usually contain electricity as one of the elements. mostly a manga reader here.

In antiquity people probably considered it a form of fire since anything struck by lightening tends to burn or at least get extremely hot? Or possibly they saw it as some combination of wind and fire maybe?