What is wrong with stock buybacks?

Genuine question, I don't understand the economics of the stock market and as such I participate very little (probably to my detriment) I sort of figure the original theory went like this.

"We have an idea to run a for profit endeavor but do not have money to set it up. If you buy from us a portion of our future profit we will have the immediate funds to set up the business and you will get a payout for the indefinite future."

And the stock market is for third party buying and selling of these "shares of profit"

Under these conditions are not all stocks a sort of millstone of perpetual debt for the company and it would behoove them to remove that debt, that is, buyback the stock. Naively I assume this is a good thing.