Actually Bitcoin price often influence altcoin price but there's a season where altcoin do extremely well even when Bitcoin is stagnant or declining. What if this season comes More often, what will be the faith of Bitcoin?
Altcoin is controlled by its core team. If a project team takes care of their coin and provides large liquidity and can create hype on the token in the market by buying back and burning tokens as well as partnering with big companies etc. And the coins that are in the top position most of the time depend on the market trending and the price goes up and down depending on the movement of Bitcoin and also from some intervention of the team.
When the price of Bitcoin starts falling, there is a lot of volatility in the entire market. Because everyone is afraid that the market will enter a bear season, many people start selling their holdings, due to which the prices of other coins are seen to fall even faster because Altcoins have much less liquidity than Bitcoin, so their volatility is much higher. If the price of Bitcoin remains stable, then the prices of Altcoins get a chance to increase.