Inflation adjusted dsta just comes to tell us that either eggs have been outdoing the CPI for 25 years or that actual CPI is way higher than what the BLS calculates.
Or a third option: eggs are just a terrible proxy for CPI
CPI tracks a weighted average of a large basket of different goods, of which eggs are only a small part. It would be extremely surprising if the change in egg prices over time closely matched CPI.
It depends what dates you're looking at, but energy (gas prices and more) and food (including eggs) are generally recognized as way more volatile than the rest of the CPI.
Eggs were actually quite stable for the 20 years prior to 2001, so maybe don't put your life savings into egg futures...
Egg prices: https://fred.stlouisfed.org/series/APU0000708111
CPI: https://fred.stlouisfed.org/series/CPIAUCSL
Core CPI (without food + energy prices): https://fred.stlouisfed.org/series/CPILFESL