It's always been unclear of what causes that correlation in price with Bitcoin and altcoins but the biggest pointer has been the fact that altcoins are traded in Altcoin/BTC pair so it makes it super easy for them to be directly affected by everything that's happening with Bitcoin since BTC is their secondary pair. While doesn't happen all the time, it does for majority of the time.
That's true but there are coins that don't yet have Bitcoin pairs but still get affected by the movement of Bitcoin and this is because the whole cryptocurency industry is built around Bitcoin. If bitcoin fails tomorrow, I don't think the industry will survive or it will take a very long time before the industry recovers as trust will be lost. Traders look at the movement of Bitcoin before decision are taking in the altcoins market weather to sell or buy.
With this mentally, the market is automatically program to react to Bitcoin and couple with the fact that majority of the altcoins has the highest trading volume with Bitcoin. Untill recently the stablecoin pairs were not having much trading volume but that is picking up quick rapidly. With time, Bitcoin would be having less effect on the general market as the stablecoin pairs becomes a prefer choice of trading instead of Bitcoin.