Why do people burn Bitcoin or other cryptocurrencies?
Counterparty coin is one instance I can recall that they burned 20+ bitcoins to prove they are "serious" about their project and from those burned coins they generated counterparty tokens. These tokens can be seen as proof that they are linked to burned bitcoins, but obviously doesn't give them the same bitcoin value. It's more of a: "Hey, I'm serious about my project. Here's proof that I'm going to work on my project by throwing away money, but I'll also generate new coins in its replacement".