Demand for things like horse meat is limited. Even if a butcher gave it out for free, they wouldn't be able to "sell" as much horse meat as chicken meat, at least not for human consumption.
So, when you realize you're already selling the maximum possible amount of your good, you're only option to increase profit is to increase your prices.
If your market reduces even further (say, 10% of the people buying your horse meat die of old age), you will often have to increase price even more to try to keep the profit you were making. Especially with goods like meat, where the supply side is also inelastic (you can't produce half a horse, you butcher a whole horse or you don't butcher it at all).
For niche culinary products, this type of extremely limited market can actually exist. I'd bet if you were allowed to sell mouse meat, you would quickly get to know every single person in London who wants to eat mouse meat.
Of course, I'm not claiming that demand will not be reduced by price. You can't charge a million dollars per kilo of horse meat. But you also can't expect to increase sales volume for certain niche goods past a point, regardless of price.
Edit: this is also often visible in the price of seasonal specialties. For example, in my country, lamb is only commonly eaten for Easter. So, demand for lamb spikes around Easter every year. But, lamb prices actually drop around Easter (at least for consumers) - the rest of the year, lamb is only sold at high prices for the few people who consider it a delicacy. But around Easter, as demand increases for cultural reasons, competing on price starts making sense and price drops just as demand rises.