It's the age old question, why can't we tickle ourselves? If you rub your fingers along your skin, sure there's sensation but you don't break down into a laughing fit (at least I don't :P), if someone else does it to you, you're rolling around on the ground begging them to stop tickling you.
Why is it that other people can tickle us but we can't tickle ourselves by touch? (I'm aware that if you use a feather or foreign object on yourself you can be tickled by it so that doesn't count.)
In short, it's because your brain processes external and self-produced stimuli differently.
If someone tickles you, you feel that ticklish feeling, but when trying to tickle yourself, there is a reduction in the sensation. When you are tickled by someone, a part of your brain activates causing you to laugh, etc., but it seems that when you trying tickling yourself, your brain doesn't react the same way and that section of the brain does not activate as if someone were tickling you.
You can't tickle yourself because your brain know that it's you. Your cerebellum knows that it's you, and so you don't feel it. Your cerebullum "predicts" that you are going to experience a tickling sensation (as you put, "a laughting fit"), and rushes to cancel out the other parts of the brain that is going to make you break down into laughter.
In other terms, tickling is 'controlled' by two part of the brain, the touch cortex (somatosensory) and the pleasure cortex (anterior cingulate). When you are tickling yourself, these two regions are fired less than when someone else is tickling you.
Basically, your brain is thinking "Why is this person hurting him/herself?" and rushes to cancel all the sensations you can feel. Only when someone else tickles you (and their brain is not connected to yours) can you start laughing. It is, in a way, unexpected when the tickle monster attacks you.
Sources: https://www.scientificamerican.com/article/why-cant-a-person-tickle/
