heh I've given it a go. People say it isn't possible to tickle yourself. This is somewhat incorrect. Over the past few years I've studied as much as I could on what makes tickling go round (even if I wasn't interested in it this way I would still be curious WHY tickling exists). Tickling is a nervous reaction. Either the person is not used to being touched in a spot or they are used to being tickled when being touched in a spot.
Example A) Person is never really touched around their abdomen or under their arms. Suddenly they have a bf/gf who starts tickling them there. As a nervous reaction they laugh because they are not used to this.
Example B) a person gets touched in a particular place quite often but either under certain circumstances (like them being tied up or the person who is about to touch them laughing maniacally or wiggling their fingers) or simply every time they get touched there it is to be tickled they will have the same reaction.
This said, the main reason you cannot tickle yourself is because you are pretty used to touching your own body in almost all places and you are completely aware of what sort of motivation is behind you being touched. No surprise, complete comfort and security... no nervous reaction.
Now, for me this isn't 100% true. Through my life I've never found a particular reason to handle the bottoms of my feet with my hands (they are kind of sensitive and usually the only times I've had to run my hands down them was to find some kind of injury). As such they are not even used to being touched by me and when I do touch them, I get a nervous reaction because I've trained myself to cringe whenever I do it (expecting to find injury). So when I run a finger down the bottom of my own foot, I can illicit the sensation (slightly) of being tickled. Enough to give myself a grin. Sadly this wonderful gift has been granted to a person who hates being tickled.

For the most part it is an irritating feeling. It can make me grin and ALMOST cause me some cough of a chuckle, but after my hand has been there more than 10 seconds my foot becomes rather used to it.
So the idea that you can't tickle yourself is based entirely on the concept that you've put your hands everywhere and are completely comfortable with placing your hands there.