But after they buy back their shares they can later sell them on the market, right?

Or do they instantly destroy them as they buy them back?

Either way the result is the same, they can buy them when they are cheap and resell/emit them when they are expensive. And they have internal knowledge of the company. And that's insider trading.

As I understand it a company does not generally hold its own stock like other investors do [0]. You should think of it more as a sink/source for the stock. So the company can just arbitrarily create as much of its own stock as it wants. Obviously doing this will dilute existing shareholders, so companies won't do this unless there's a good reason to. Likewise, when the company buys back stock, that stock just disappears, so now every other shareholder has a larger fraction of the company.

[0]: I think the main exception here is that there might be an employee equity pool. The board will approve a certain number of shares to be created for the pool, and then they'll sit around and gradually be transferred to employees as their stock grants vest.

I suppose it's true that there is trading happening and there are insiders who are doing it, but that's not what "insider trading" is. A company can use its own information internally to benefit shareholders and it's perfectly legal. Insider trading is when you learn of information that doesn't belong to you. It's a violation of trust.