Actually , even in a great defensive battle of Midway Americans used their fleet carriers offensively . They formed strike packages and struck enemy . Soviet tactics was completely different , they never planned to use Su-33s as attackers . Instead , they would form CAP and wait for the enemy . In this regard , Kuznetsov is more like escort carriers of WW2 .
In simple terms , in American doctrine , aircraft carrier is a sword and AEGIS destroyer or cruiser is a shield (Aegis is a shield of Zeus in Greek mythology ) . In Soviet doctrine , heavy bombers and subs like Oscar II were sword . Kuznetsov-class along with some other platforms would form part of the shield .
Midway is a case, as I pointed out, where the US Navy was using its carriers to defend Midway. It did not send them offensively off towards Japan to do a seek and destroy mission. That would be pure offensive operations.
Those carrier laid off Midway because they knew the Japanese were coming to them. And the Japanese were on the offensive. And the US knew it, because at that point they had broken the Japanese code. But they did not know the exact locations so they had to send aircraft out to find them. When they did find them, of course they attacked. But they were attacking from a defensive posture.
Now, during the great battle of Leyte Gulf, the US Fast Carriers did go out hunting the Japanese carriers...and the Japanese lured them into to doing that...and Admiral Halsey took the bait. It was a massive and complicated operation the Japanese planned...the biggest naval battle in history.
When Halsey took the bait, as the Japanese planned, it allowed the Japanese force which was tasked with breaking through to the invasion force to do so. And they succeeded in breaking through and would have ravished the anchorage had not the Taffy Escort Carriers and their destroyer escorts put up such a savage fight in the Battle off Samar. As it was, it is the only time a US carrier was ever sunk by open gunfire from Battleships and cruisers. But they put up such a fight...and it was a ruse...that the Japanese Admiral turned around and left, right at the point of accomplishing his objective. He just thought he was fighting a far larger force and felt he could not get through.
So, the doctrine is not so straight forward.
The US has used carriers defensively, and still has the strategy to do so when necessary. And the US Navy practices that strategy in exercises to this day.