The private sector have a responsibility to help fight terrorists because they protect their people during their war and they are enemies with whomever they go against. The private sector responsibility is to protect the Homeland and defend their defenses. The private sector promote freedom and human dignity and to get that they fight to protect their people.
Fighting terrorism requires a coordinated strategy and therefore needs to stay in the hands of the government where efforts can be thought out and coordinated between different departments. If the private sector starts fighting terrorism, there will be a lot of different, uncoordinated and possibly contradictory efforts and while the efforts may be undertaken in good faith, they may result in more harm and confusion than good.