I get tickled easily on the soles and armpits. Only when done by someone else. Its a violent laughing reaction.
Do it to myself…nothing.
Why?
It’s basically because your brain predicts the sensation when you cause it yourself and cancels out the tickle response.
Researchers have designed “delay tickle” machines that delay your movements. Imagine basically a tickle stick, like a stick with a feather or foam on the end of it. With no delay, the stick moves exactly as you move it, and you get no tickle response. But once you increase the delay to where your brain no longer predicts the tickle sensation, the brain no longer blocks the tickle response and you can effectively tickle yourself.
If I remember correctly, it takes about a quarter to a half of a second delay to trick your brain so that it no longer blocks the tickle response.
Somewhat addressed in this Cecil column from 1983:
I actually find that I can tickle my own feet, which is really annoying when I want to scratch an itch on the sole, no where else though.
Wonder why that is?
I would point out a machine cannot tickle either. If you are trying to get comfortable on an airplane seat, the vibrations might annoy you, but they do not tickle you. Your vibrating phone cannot tickle you either.
But, but…if you see Uncle Billy approaching you with an evil grin and his grabby fingers flexing, don’t you anticipate the sensation then as well?
mmm
Because your brain processes the actions needed to tickle yourself, and it does that far faster than it can process the actions of someone else that will probably lead to tickling. But that other person’s actions also need to be sudden and quick. If someone says to you, “I’m going to tickle you now,” and then slowly moves their hand towards you and makes the exact same movements they would usually use to tickle you, it doesn’t work.
You have to make a tickle sudden for it to work even on a child. You can go “I’m going to tickle you!” and make repeated movements as if you’re just about to do it, and then suddenly strike, and it works as a tickle. The child’s brain knows it’s going to happen, but not exactly when. It needs to be sudden, but preferably not too sudden, because then it’s just terrifying 
This may also be the reason why children are easier to tickle than adults - their brains haven’t got used to making those predictions yet.
It does seem to work when you tickle the roof of your mouth with your tongue.
I’m so freaking ticklish (as in, freakishly ticklish…) that I used to be able to tickle myself unbearably by taking off my shoes and socks and thinking hard about how the air felt on my bare soles (shudder)
However, it’s certainly *harder *to tickle yourself than to be tickled by another person. I attribute at least some of this to a stress response. If I grab myself in the armpit or the neck it produces a lot of the same tingling hairs-standing-on-end feeling as being tickled there by another person. But I know I can stop any time I like. I have no such iron-clad guarantee if it’s another person doing the grabbing. This heightens stress, and stress makes me a lot more sensitive to any physical stimuli
Consider masturbation. If your explanation for why you can’t tickle yourself would, by extrapolation, also imply that you can’t get yourself off, you will need to elaborate on your original reason.
Just sayin’
And of course, upon reading, we all tried this.
I noticed that I can avoid the tickle reaction if I relax my muscles in the area involved. It only works if I expect it and concentrate. If I don’t expect it, I get tickled.
I get the impression that people who are ticklish can’t avoid tensing up.
Well, I don’t think the element of surprise is a necessary component of most people’s non-masturbatory sexual experiences, so I’m good.