How do you insert the wires into the pull fan switch so they don't pull out

Usually you leave the pigtails (the attached wires) in place and wirenut or use an insulated crimp to the ends to another wire.

Is the switch a push in pull it setup? Many of electrical switches " like the back of newer outlets" have a hole to push the wire in and also a very small hole beside it to release the wire and sometimes to help the wire go in easily. If you can describe the switch better it would help.

Happy Holiday!

"Tinning" the strands with Solder will help.

Good point Stratmando. Hope fully we will get more info happy holiday

The wires have to be "tinned" as Strat said. Usually they already are from the old pullchain.