Use the point of a spudger to push on alternating sides of the connector to "walk" the JST connector out of its socket.

It may take a lot of alternating before the connector comes out. Be patient, and don't pull on the cables.

If that doesn't work, use a pair of tweezers to firmly grip the sides of the connector and pull straight away from the socket. Hold the tweezers closer to the connector to get a better grip.

If you're having trouble, try rocking the connector side-to-side to loosen it.

Remove the fan from your laptop.