Why cant you find neutral in your 1981 Honda ct110 when you can find every other gear?

Neutral should be found all the way down. (Pressing the front of the gear shift lever down as many as 3 times.) If it cannot be found, it is probably an internal matter which can be corrected by removing the right transmission cover and working your way to the gear selector and drum.

Its possible that the little pin that the internal shift mechanism grabs could have broken as there is one for every gear and the one that the shift mechanism grabs for neutral is gone or broken. its is very easy to replace and should not be a costly part.