The big issue with debit cards is that because the money gets pulled directly from your bank account, a big fraudulent charge can trigger all kinds of fees. While you might be able to get those fees refunded, it's more like to be a hassle than simply disputing a fraudulent charge on a credit card.

For example, my bank account usually has about $1000-2000 in it (I keep most cash in savings at another bank for their better rate). My credit cards and electric bill all pull directly from my bank account via ACH, and I write a monthly rent check. If somebody puts a $2000 fraudulent charge on my debit card, I might get nailed with a monthly fee for going under my $500 minimum balance, an overdraft fee, and a returned check fee if my rent check bounced. My autopay ACH transactions might also not go through, causing my credit cards to charge me late fees and interest, and the electric company to charge me late fees.

Some banks may have protections against all these things for debit transactions, but I strongly prefer to just stick with a credit card, because I've never had a problem disputing a transaction there.