There are a lot of advantages to paying for a flight with a credit card. One advantage is that you are protected when you make bigger purchases. For example, if you spend more than $100 on a flight, you will be covered for a refund if the airline or travel company goes out of business. This will not necessarily be the case if you pay with a debit card so check first. Credit cards are also more useful for spending in a foreign country and give you better exchange rates than you would get with your debit card.
Certain credit cards will offer you air miles for each sum of money spent, thus saving you a bit more on your flight tickets. They may also give you a certain amount of cashback on the purchase of your flight ticket.