Bitcoin prices will never be stable, because bitcoin has a very strong influence from very limited supply and very high demand making bitcoin very difficult to be stable there will be price movements because of the influence of buyers and sellers interacting with each other.
Yes, bitcoin is known for its volatility and bitcoin price will never become stable, this made bitcoin very popular now. And because of big investors manipulating it, being stable will never happen.
there is no point in making bitcoin stable, with its fluctuating nature, bitcoin makes traders interested. basically if purchase and sale are same, price can be stable, but it is very difficult to control like that