What is the point of sterilized QE?

Since the point of QE is to inject liquidity into the market, what is the point of sterilized QE? It injects liquidity by purchases, and then removes that liquidity by a number of ways, including borrowing the same money it just used to purchase with and offering a rate of return on that, selling Tbills to banks who purchase them with the same money, and so on.

So, I buy something from you so you can have money, but then I borrow that same money back from you. I don't get it. Please enlighten me someone...