When we are tickled by someone else, the sensation causes a form of anxiety or panic, as does not knowing where we will be touched or tickled next. Certain types of laughter stem from nervous reactions like anxiety and surprise. Hence, laughter is normally an involuntary, non-aggressive response in this situation.
The surprise and tension happens when the tickler initially strikes and the laughter is an relief and reaction to that process. The reason we do not stop after the initial touch is because we do not know what is going to happen next, so the brain is tensed in anticipation of the tickler's next movement. Our body is actually in a state of panic & doesn't know what to do. The reason we squirm is because our body is trying to escape from whatever is tickling it, not knowing whether or not it is going to cause any harm.
The reason we do not laugh when we tickle ourselves is because the brain is already aware of what is going to happen and where, thus there is no surprise and no need for tension.