[JohnBooty]

    There are no missiles capable of loitering.

Blatantly incorrect, and I'm not sure what you wrote that in response to? https://en.wikipedia.org/wiki/Loitering_munition

    The reference to Midway is odd because without aircraft 
    carriers the U.S. would have lost the battle.

Aircraft carriers were obviously the dominant force in the Pacific, almost a century ago. No argument there. There was really nothing to counter them, except fighters launched from other aircraft carriers.

Whether we're talking about 1942 or 2024, aircraft carriers can't perform evasive maneuvers and launch/land fighters simultaneously. You pretty much can't land a non-VTOL plane on a carrier doing anything but traveling in a straight line into the wind.

During the Battle of Midway, the USN fortuitiously exploited this weakness more effectively than the IJN. It was a big factor in the US victory.

    [Carriers] aren’t obsolete

As has been stated by myself and others multiple times: they're not entirely obsolete and still serve an important purpose. The vast majority of potential adversaries are not peers or near-peer capable of advanced missile attacks.

But if you don't think a carrier group is extremely vulnerable to a superpower with advanced missile technology, you might literally be thinking in 1942 terms.

    I don’t believe you are well versed in modern naval 
    operations. I’m not either 

One of these statements is correct.

[skhunted]

Those that are big enough to do major damage to an aircraft carrier can be intercepted by aircraft. Which is what I referred to when I mentioned air dominance being the key in this case.

There are no loitering missiles. If you read the wikipedia link you'd see this written:

Loitering munitions fit in the niche between cruise missiles and unmanned combat aerial vehicles (UCAVs or combat drones), sharing characteristics with both.

Aircraft carriers matter greatly in peer to peer naval supremacy. China is building aircraft carriers to contest the seas around Taiwan against the U.S.

You are not well versed in modern naval operations. Neither am I.

[JohnBooty]

I'll point out a few of your errors, no time for them all.

    Those that are big enough to do major damage 
    to an aircraft carrier can be intercepted by aircraft

Quite a few in this sentence alone.

Hypersonic cruise missiles exist. These are as fast or faster than air to air missiles, making interception tricky to say the least: https://en.wikipedia.org/wiki/Hypersonic_weapon#_China

Ballistic missiles are also generally going to be traveling at hypersonic speeds. As they descend at steep angles from space. Even tricker than cruise missiles traveling somewhat horizontally.

Third, a US carrier hosts about 40 fighters. During high tempo operations a single bird might be in the air up to 10 hours a day or so, but this tempo can't be sustained for long - it's not like you can have 40 simultaneous fighters in the air 24/7. Planes need maintainence, etc. Surely even you can understand that there is a limit to the number of simultaneous missiles these fighters and the rest of the fleet's defenses can intercept. There are a lot of variables that go into that number, and we're talking about classified and rapidly-evolving hardware, but I don't know that anybody thinks it's more than a near-peer could throw at a US carrier group.

     China is building aircraft carriers to contest 
     the seas around Taiwan against the U.S.

This is all speculation, unless one of us literally has access to what China's military planners are thinking.

But: no. I'd suggest looking at a map. Taiwan is less than a hundred miles from China's mainland. They certainly don't need aircraft carriers to fight a war in the seas around Taiwan. Come on.

They are, in all likelihood, primarily planning to use those carriers for force projection elsewhere in the world. (And/or for prestige purposes)

There are some informative answers from others in this thread; you would do well to learn about this topic if it interests you.