KMC chain disconnection issue
Pins can be forced out from both sides.

Quite a lot of force needs to be put on a pin to force it out, especially at first to move the pin out of its interference fit in the outer chain plates.

Make sure the chain is positioned in the chain tool properly, and the driver is hitting the chain pin straight-on. If you have a small chaintool, such as one from a portable tool kit, you won't have much leverage. You can hold the tool with a large adjustable wrench and turn the handle with pliers. 

Don't be afraid to really force it. IF you are replacing the chain you wont break anything you care about. 

If you want to re-use the chain you need to careful if you have unsuccessfully tried forcing more than one pin out. You may have moved a pin slightly and weakened it. If you suspect you have done this a new chain may be a safe option. 

I linked a Park Tool video on replacing a chain below that includes how to break a chain.