No one even mentioned the word compression and it makes me wonder about you people If the engine turns over without a plug in, it's because there is little resistance to turning over in a well oiled engine. With the plugs in the pistons now must generate compression of the air fuel mixture and this takes much more force. The power supply may be adequate to turn the engine over without plugs, but it may not be adequate to turn the engine over with plugs in. MAKE SURE you jump start CORRECTLY, with very good contact on terminals(you must have the right voltage which takes any contact, but right amperage as well which takes sufficient contact to pass that much currently in a given time which is why battery terminals are the size they are and not tiny wire connections) The engine should easily enough turn over with a breaker bar and socket on the crank pully if there is an easy way to verify this(only rotate it forward) if it takes a lot of resistance the engine is gummed up or starved for oil(or sludged) and good luck at this point.

You could uscrew the plug and remove it and the extension rod, and then examine why the socket gets stuck on the plug. A worn or ill fitting socket may be the problem. If the socket does not have a detent that mates with the little spring loaded ball in the extension rod, get a better socket that has only 6 points. Do not use a 12 point socket as these are more prone to rounding the corners of hex nuts and jamming. You may have to resort to an extraction/pickup tool. The ones I have fit over the outside of items; You need one ths fits into holes and it has to go into the 3/8 drive hole in the socket. Also, there must be enough room inside the socket above the spark plug to get the tool in there. My first choice would be to get a good socket that comes free of the plug after it has been tightened. If the O.D. of the socket fits too snugly with the tube, a little dirt and gum in the tube will give problems. Get a thin wall deep socket.

It wouldn't hurt to replace the receptacle....if it's older, chances are the contact's poor and would be contributing to the arcing, in fact, if it is bit marginal and is wired in the backstab (where the wires are just stripped then pushed into the back of the receptacle, not wrapped correctly around the screws on the side, that may contribute.

Been using copper Autolites in my Briggs and Tecumseh engine's with good results so far. I've had an NGK iridium in my Yamaha Tri-Moto 2-cycle for over a year now and it's been great