That's easily doable, at least here in the southern US. I regularly buy $10/3lb of chicken tenderloins. You can do much better if you're prepared to buy in bulk. Of course, venison is cheapest, if you're willing to kill it yourself/eat fresh roadkill/get the excess from hunting friends. ;)
Catfish runs about the same here as chicken, but tilapia can be had for super cheap. Of course, that's another one you can get for almost free after the investment of a fishing rod and a weekend.
Your egg prices are insane. I can buy 60-packs of eggs for $8.72.
The comparison isn't quite apples-to-apples as legs have bone, but I can't imagine I'm paying over $1.50 or so for the meat.
Note for non-Atlantans: we don't know what "Farmers Market" is here, this is basically a large grocery store with a good produce section.
Prices are from AH, one of the more expensive supermarkets here. [0] Chicken breast is $6.50 per kilo, no bones just the breast, or indeed ~$3 a pound. 100g serving is recommended here, but then that may be the difference between Europe and the US.
Ground beef is even cheaper. Of course these are the lower-end prices, you can pay $20 for a kilo, too. But for the cheaper prices the meat is still excellent as AH is one of the most expensive supermarkets.
The cheaper supermarkets here, which are still decent quality overall, get you a 10-20% discount. The cheaper shops have small discounts (5-10%) on things like meat or salmon as we don't see a lot of branding premiums here on meats. And bigger discounts (15-20%) on things like ketchup or cola, where if you buy a no-name brand that tastes just fine you pay a third less.
Wouldn't have thought the US had more expensive meats. When I was last stateside I remember paying a pittance at the golden coral and leaving with the feeling I just ate 5 cows for the price of a cinema ticket! How they remained profitable boggled my mind at the time, even with cheap & absolute garbage ingredients I must have cost them some that day :P
Eggs are as cheap as 15c and as expensive as 40c an egg. So a dozen can be less than $2.
Two things must be mentioned... one is that it's not a purchasing power parity comparison. I'd say average wages are a little lower in the Netherlands than in the US (although I think the median family is a lot better off here), meaning there's a bit less to spend here, putting cheaper prices here on some foods in perspective.
And the Euro is abnormally weak right now which is likely a temporary thing. Normally the Euro is about 30% stronger, so any price conversion I do now would normally be 30% higher.
Where are you buying your protein for $3 per pound? Ground beef costs more. 100g before cooking is a pretty small serving.
My local Safeway wanted $7/dozen (!!) for store brand eggs last week. I walked away shaking my head. Dollar isn't what it used to be. This week it was a "more reasonable" 5.49.