In a greater philosophical sense - economics started off as a branch of philosophy - money is equivalent to favors you have earned, by doing things that the rest of society valued. Depending on how well society values your work (based on supply, demand, and your and your class’s ability to negotiate a slice of the pie with your employer), you might get more or less money, but we interpret that as equating to “here’s how much you gave back to society.” And the value of the money is in saying that you can gain from others an equivalent amount of labor back, towards your personal safety and happiness. Money is a debt that society owes you.
When you burn the money you are, in essence, allowing the rest of the economy to forget their debt to you.
Now, if you are a person with great plans for society - you could have figured out how to cure cancer, if only you had had capital sufficient to finance the R&D - then that’s a loss to society. You could have used the debt you held to bring in others to help you, and now that opportunity has been destroyed.
More often, one would expect that you would use that money to a) keep yourself alive, so that you can continue contributing to society, and b) keeping yourself happy, so that you want to continue contributing to society, making the world a better place in at least a small way, even if it’s not curing cancer, or c) loan the money to someone who wants to find a cure for cancer, or otherwise do something that everyone in society would appreciate.
By destroying the money, while you are freeing society of its debt to you, you’re now destroying your own ability to survive and to keep yourself enjoying life by at least some amount, and destroying the ability for that money to help others.
How it all balances out will depend to some extent on why you burned the money, but in general it is a negative.
Now that was more just the philosophical side of things. Getting into more modern macroeconomics, then you start needing to understand how most of money exists.
The majority of money in the economy exists as a debt owed to a bank. Either a customer/business facing bank has loaned out money - probably going into debt on their end - or the central bank has loaned money to a normal bank - definitely going into debt to do so.
Allowing banks to go into debt - in essence holding a negative quantity of cash in their coffers - is something that is seen as “okay” because something like 98% of people who take on loans pay them back. So the total debt load is actually quite a bit smaller than it seems, in an actuarial sense. And then, further, the banks charge interest. This allows them to recoup that final 2% that the defaulters didn’t pay (plus make a bit of profit). And, overall, loans are good because they give people the opportunity to put grand visions, that will make the world a better place, into effect. To be sure, most “grand visions” are just a new restaurant. But the population is growing, and food does make people happy. The world does become a better place, thanks to loans.
On the side of the central bank, they’re less concerned about recouping their debts…because magic. That goes back into philosophy, but basically comes down to making the world a better place and having a military.
Every year, more loans are taken out, for larger sums, than in the previous year. And loans often have a period of 20+ years. It goes out faster than it comes back in. In result, most money that exists in the economy exists as money which was created by a loan and which hasn’t been paid back yet. And that quantity grows from year to year.
When you receive money, you’re receiving money that was loaned out to someone. That person had a dream. They expect to be able to recoup their money, based on putting their dream into action. Their dream will, necessarily, be a money-making venture since that’s how we encourage people to do good work for society. We allow them to profit off of them. We’ll call this someone George.
George wanted to build a new restaurant. He took a loan, built his restaurant, paid you to help construct it, and now you have burned the money.
Had the money continued to exist, then it could have gone back towards buying food at restaurants, like George’s and helped George to pay off his debt to the bank. But, that money having now been destroyed, it can never make its way back to George or anyone else who owes money to a bank.
Overall, this raises the risk that George and others will default on their debts, and if lots and lots of people started taking up money burning as a hobby, then it would effect the defaulting rate of debtors.
Instead of 98% of people paying off their loans, it might change to 94%.
Consequently, banks would need to raise their interest rates.
Higher interest rates then mean that it is more dangerous to try and start a business.
And so, in the end, fewer of the people with a grand vision for how to improve the world will do so.