I understand and agree with the general message above to always book with the airline, as it does give you the most chance of getting a rebook or change if something goes wrong. However:
Sometimes resale agents will buy up a block of seats at a specific fare. There are cases where you can get a much lower fare if you find one of the resale agents trying to sell their seat, esp if you book last-minute and they either sell it or lose it. This is a case where Skyscanner, Priceline, Kayak, etc sometimes can find oddball listings that you won't get on the airline's own site.
The other reason to use an agent (that I've personally run into): many airlines require showing the credit card used to purchase at check in, if you are in a higher-fraud-risk country. If you are buying a ticket for someone else and won't be at the airport with them, it may be inconvenient to do whatever alternate authentication the airline requests (for example, I've had to go to the airline ticket office and sign docs and have them check my ID). If you book through a booking site/agent, the site/agent takes the fraud risk and the airline won't need to check anything. As most of you are US-based, probably not a big issue. This card verification can be very common in Asia.