When people say 'first strike' in this context, they mean 'nuclear first strike', as in 'launch enough nuclear missiles to take out your enemy's ability to fire back'. The reason for nuclear submarines is to largely eliminate this possibility: even if you completely destroy every military installation in the USA, there is going to be at least one submarine hidden somewhere that will be able to flatten a few of your cities.
MAD only works as a deterrent if there is a very small chance of getting away with a first strike. If you can shoot down incoming ballistic missiles, then you might be tempted to launch first and just shoot down the retaliatory strike. If you can fire missiles that are fast enough that the enemy doesn't have time to order a retaliatory strike, then you might be willing to live with a couple of submarines shooting at you, especially if you have a good idea of where they are and can have aircraft ready to launch interceptors flying above them.
Aircraft carriers completely suck for launching nuclear missiles (and the USA has not confirmed that they even bother putting them on board), because they're a big obvious target. If, for example, the USA put a nuclear-armed aircraft carrier near Russia, then you can bet that the Russian second-strike capability would be on alert and ready to launch unless they got regular confirmation that the US carrier hadn't launched. Aircraft carriers also suck for second-strike, because they're too big to easily dodge a nuclear strike and so will be on the list for first-strike targets.
They're good for a conventional (non-nuclear) first strike, because they give you a staging post that you can put right next to someone else's country, but that's less of a problem for global stability. A non-nuclear first strike commits you to an expensive war. Aircraft carriers aren't also specifically first-strike weapons. They have support roles and are even occasionally used for disaster relief (a big portable nuclear reactor turns out to be quite handy sometimes).