Acuracy of carbon dating
What does change is how much warm water is close to Antarctica.During a glacial period (ice age) the oceans near both poles are much colder so the amount of heavy oxygen is very small.It is like counting the rings on a tree, but it is actually much more accurate.It also tells a much larger story than a tree (or forest) possibly could.Then the layer the year after that tells the story of that year. Scientists then measure each layer and count down how many layers they are from today.
There are very few corals in that part of the world.
When the the northern hemisphere is warmer (like now) the oceans have a higher sea level and warmer water is closer to the both poles.
Even if a location in Antarctica stayed exactly the same temperature for 100,000 years, the ice core at that location would tell the temperature record of the ocean that evaporated the water that fell as snow at that location.
Another way to explain it is how warm the ocean is near the location where the ice core is from.
The less heavy oxygen there is, the colder the water is near the glacier.
In this way ice cores do not reflect the temperature of the location they are drilled.