Because I get an interest free loan for somewhere between 20 to 45 days which with I can earn interest on (currently 2.25% per year), and I get an additional minimum of 2.5%+ cash back on the amount I purchase, and I get the ability to call up a bank and dispute a payment if a merchant tries to screw me.

And various other benefits such as airline and hotel status.

I don’t see a reason to turn down free money.