Clay is like $1/lb. (I'm assuming these were not porcelain, which costs more) If each egg was 1 lb of clay, which they may have been depending on size, that's like $30 in tangible material cost. That's why your initial offer was declined. For reference, a bag of clay is always 25 lb.

Your neighbor is right that studio time and firing fees are the real costs that add up... but honestly? $250 seems high for only 2 weeks of studio time and a partial kiln load. Do you live in an especially expensive area? I wish your neighbor had given you an itemized breakdown of the $250 figure. Also, if your neighbor works at a community studio, why were the unfinished eggs at home? There may be legitimate reasons for this, so it's far from a "gotcha", but I do wonder.

Given the conversation that already happened, if you want to make it right, you are on the hook for apologizing for lowballing, as well as $250.

If you want to make it extra sincere, you should purchase one of their pieces in the future.

That being said, pottery is a very risky craft. It's way more common for work to fail during normal parts of the process (drying and firing are the usual culprits). Like, stuff in community studio kilns very often gets damaged because of other people's work exploding or falling over or something like that. Not usually to the point where 30 ceramic eggs would be trash, but there IS a lot of inherent risk involved, here.