That is not unusual.
Caused by a variety of reasons. There is not enough voltage to crank the engine and make spark at the same time. When you let off the starter, the voltage comes up enough to make sufficient spark, and the engine starts.
Could be a failing battery, partially discharged battery, poor connection. Have the battery load tested, feel for hot connections after cranking.
Possibly the starter is drawing too much current, usually from worn bushings. Typically it will be cranking slow, heating the battery cables, usually worse when the engine is hot.
Could have the wrong coil or coil/resistor combination. If it has a true 12v coil it should not have a resistor. If you have an ohm meter, check across the primary terminals of the coil out of circuit. Should have around 3 ohms resistance. If there is a resistor, the coil and resistor in series together should have around 3 ohms.
Could also just be weak spark in general. A failing coil, bad wires, worn or fouled plugs, bad cap or rotor, points out of adjustment, bad condenser, worn distributor bushings. It should give 1/4 blue hot spark at the plug end of each wire to ground while cranking. I'll bet you don't have that now, for whatever reason.
Another cause, (but since you tried a wire from the battery, you eliminated this) is a failing ignition switch. Especially with a switch that incorporates a start position. Sometimes the switch will loose the ignition circuit when it is turned to the start position.