it makes some effect for bitcoin prices or not if 1 of the big pool closed?
No. Mining is affected directly by the price of bitcoin. The price of bitcoin is not directly affected by mining.
This has been stuck with me for a few days.
Is it due to the volatility, arbitrage market, that miners see an affect from fluctuations?
Large scale miners are affected because most of their inputs to mining (e.g. electricity, rent, cooling, staff, hardware) are priced in USD (in the USA). That means when it comes time to pay the electric bill, or staff wages, or rent, they may need to sell some BTC to do so. They may find they have less, or possibly no, BTC left over. Small scale home miners don't have the same constraints, but they may also decide not to subsidize their mining "hobby" forever.