They demand the same amount of the same quality food, which gets more expensive because of inflation.

^this. The currency is being devalued and is worth less and less per unit. So the same way that you’re experiencing your paycheck buying less and less, so the farmer’s income is also buying less and less and hence he has to put his prices up.

Farmers need to charge prices that enable them to support all of their rising costs. Whether their costs increased to produce eggs or not, their costs in general have gone up.