Not everyone pays their balance in full every month. They may not make interest off of you or me but they do make interest off of a lot of cardholders. In many cases, the interest is variable and the larger your (running) balance, the higher your rate. If you're close to your limit and making minimum payments, you can literally take decades to pay off $2,000 or so.
Some people don't pay at all every month and end up paying late fees. Some people use their cards overseas and pay foreign transaction fees. Ever take a cash advance? Me neither but they charge you interest right away for that instead of waiting until your statement. The list of fees and charges is as long as my arm and in tiny print. That's how they make money.
The points/bonus/cash back and other rewards programs are to get you in the door. It's like when you see a luxury car advertised for a "too good to be true" price and you get to the lot and find out that the one they are selling for that price is a manual transmission without AC or a radio, they only had one and they sold it an hour before you got there. It got you on the lot though. The rewards programs function in much the same way (minus the disappearing part), they get you interested in their offering among a sea of virtually identical products but rest assured, if the card issuers were losing money because of them, they wouldn't exist for very long.