Counting layers may sound easy. After all, the top layers are almost a foot thick. And, in fact, it was easy - at first.
Eventually, the counters reached layers that were grainy, or contained dust, or bubbles, or volcanic ash, or forest-fire soot, or pollen. They tried several techniques on difficult layers. For example, they used different colors of backlighting, and they checked the ice's electrical conductivity.
Worse, occasionally a section of ice would split. This happened because ice that is a kilometer down is under a lot of pressure. Bringing the ice to the surface released the pressure. The GISP2 crew lost 87 meters out of 3000 to splitting. For the same reason, bubbles have been growing inside the stored core samples, and that makes it harder to go back and recheck counts.
The deepest layers are perhaps twenty times thinner than the top layers, and of course all the problems get worse. Near the bedrock, new problems come in. The layers may be parallel to the bedrock, rather than horizontal, and geological things (like folding) are possible. Pebbles are seen. Flow to the sea can make layers shatter.
This is a high-effort proceeding, since one core might weigh 40 tons and take five summers to drill. Counting was done in cold dark rooms by people wearing "moon suits" (to avoid contamination). The people who count ancient tree rings have it much easier, and they follow rules such as "obtain two or three cores from each tree, and sample at least 20-30 trees at the site". If time and money had been available, the ice core researchers would do something similar, and counting accuracy would greatly improve.