In this episode, Jesse explains, why some clipper blades drag. 

If you've been using the same blades for months—especially pre-shaves—they're probably dull and will drag fur. It's unavoidable.
If your blades were recently sharpened, check your blade drive or lever. Andis, heiniger, or osterbolt. Wahl and A6 models. Check their condition.
I recommend every 4-6 weeks with andis. Everyone else, every 2-3 months. They just a few bucks and prevent many problems.
Having sharpened blades and a competent blade drive or lever. I examine oil next. If the blade isn't oiled regularly, it will heat up, seize, and not cut hair fast enough.
If you've been oiling your blade a lot and it's still not doing that, check tension. You can push your cutter blade out with your thumb. It shouldn't hurt your thumb or side out easily.
If it slides out easily, it presumably lacked tension and dragged. If you can't move it, it's usually over-tensioned, causing friction and seizing up.
If your blade tension, lever, sharpening, and oiling are good, Hinge next.
Any hinge that you can open with your fingernails is worn out and has to be replaced. It drags because it's not keeping the blades securely against the clipper.
Also tighten hinge screws. The screws often back out, causing the clipper to drag.
Those are some other reasons your blades may drag.