There are numerous reasons, but for starters you have much less protection on a debit card as compared to a credit card. That Visa logo on your debit card doesn't mean you can call Visa if you end up with fraudulent charges; it just means it can piggyback off Visa's payment system. That means if you end up with bogus charges, you have to call your bank, who at a minimum will almost always require you to open a police report and jump through a bunch of other hoops. Of course there are thousands of banks, and each one may have different policies in cases like these, but you can almost always expect it to be more of a hassle than going through a real credit card provider. Not to mention fraudulent charges are taking away real money from you, and if you have overdraft protection on your checking account, you can be wiped out.
The smartest thing to do is get a credit card, and use it like a debit card (only charge stuff you can pay off). Not to mention you can get cashback and other rewards.