Why can't an insulator let electricity pass?

Can't you just plug a battery into the insulator thus creating free electrons?

Batteries don't "create" free electrons. Batteries give (potential) energy to free electrons in insulators and conductors by producing an electric field that forces the free electrons a to move (create a current).

However, I have learned that the battery extracts electrons through a chemical reaction and then sends it through the wire. Here is a website explaining this. science.org.au/curious/technology-future/batteries

I'm not sure which part of the link gives you that impression so you need to tell us which specific statement in the link gives you that impression. The chemical reactions enable the battery to supply energy to the electrons entering the battery from the circuit so that they can exit the battery with more energy in order to do work in moving through the circuit.

Here is a part of the article that states this: "At the anode (which is a part of the battery) , the electrode reacts with the electrolyte in a reaction that produces electrons. These electrons accumulate at the anode." Then the article goes further in explaining how the positive terminal of the battery 'attracts' the electrons that are in the negative terminal of the battery. –

The accumulation of electrons at the anode (and removal of electrons at the cathode) produces an electric field. That electric field provides the force needed to do work to move the free electrons in the circuit. So the battery provide energy to move free electrons in the circuit, but it doesn't add electrons to the circuit.

Hope this helps.

The free electrons of a conductor are not so free. They occuppy quantum states, each of them with a given momentum and energy. The difference of energy between the states is very low, and the set of them is called a band. All the lower energy states are occupied. That means electrons going to all directions, so that the net current is zero.

When an electric field is applied, if there are available states just above the high energy electron, the energy and momentum distribution changes, and there is more electrons with momentum in one direction than the opposite leading to a net current.

In an isolator, there are no available quantum states in the band, all of them are occupied. So, the distribution of momentum doesn't change with the applied field. There is no net current.