Bitcoin's price is unstable due to its volatility. That is why bitcoin's price is so unpredictable that no one can say when it will go up or down. No one can control bitcoin's price that is determined in its supply and demand. When demand increases, the price increases, and when the demand decreases, the price decreases. So if you try to sell a considerable amount of bitcoins, you will see that it will affect bitcoin's price that it would fall.
Well, it is volatile means it changes so that is not the reason but just a synonym for unstable.
The real reason behind the price change of bitcoins is because like you mentioned in the later part of your post that the demand and supply changes very rapidly and bitcoins being an asset are not bound by any boundaries so as people start to buy bitcoins the price just keep increasing and vice versa for selling it drops.
A lot of whales also use this method to pump and dump bitcoins but now the market is getting more and more saturated which actually helps as now it is way harder to swing the market for a single whale and hence we see the price change is not as rapid as it was a few years ago.
With saturation in the market will always come stability be it any asset, like gold has so much value and is so stable because it is used and valued internationally.