It is self-contradictory because it is reflexive. That is, as a principle it acts upon itself, or it includes itself in its scope. As a principle, tolerance dictates that we must be tolerant of everything. We cannot pick and choose what we will tolerate and what we will not. If this is so, then tolerance requires us to tolerate even intolerance. Thus, if somebody is preaching or practising intolerance, the tolerant person cannot, in principle, speak out against what the intolerant person is doing, since speaking out against intolerance would itself be an act of intolerance. In other words, the principle of tolerance requires us to grant intolerant people the right to be intolerant. This is clearly self-contradictory, since tolerance cannot condone what it specifically sets out to be against (i.e., intolerance), but it nevertheless requires itself, logically, to do just that.
Tolerance as a principle, then, is clearly illogical, and therefore irrational. It is much more logical and rational to espouse intolerance, for then one does not get entangled in any contradictions—self or otherwise. Intolerance as a principle does not require us to be consistently and universally intolerant: it affords us the option of being tolerant if we so choose, and intolerant whenever it pleases us to be so. This is straightforward and clear-cut, and one has no difficulty following this principle in living one's life. The intolerant person's simple motto is: "I like the things I like and I hate the things I hate, and I will hate the people who like the things I hate, and I will make that hate known to them in no uncertain terms." What could be easier? It's black and white, like the world George W. Bush inhabits. "If you are not with me, you are against me, and so you are my enemy, and I will treat you as such." George W. Bush practised this philosophy to perfection during his presidency, rewarding those who supported him and "punishing" those who didn't. No moral dilemmas for him—and for others like him who like their world in black and white rather than in shades of grey.
And yet, …
We have the intuitive sense (beyond what the rational mind tells us) that there is something wrong with this reasoning, logical and rational though it is. Intolerance, we have learned from experience, does not work very well in practice. Religious wars, witch hunts (ancient and modern), persecution (political, religious, and social)—these are all the luscious fruits of intolerance, fruits whose flavours we would rather not have tasted. Mahatma Gandhi put it perfectly when he said: "An eye for an eye ends up making the whole world blind." We might say: Intolerance breeds intolerance in a downward spiral. One has only to look at George W. Bush's failed presidency to see the truth of this. Oddly enough, tolerance does not always breed tolerance, but it often does, and this is what recommends it to us as the superior of the two principles.
Game theory tells us that antagonism towards one's opponents is not usually a winning strategy. John Nash (the real-life mathematician on whom the movie A Beautiful Mind was based) has shown that being aware of and accepting (we could say "tolerating") the play strategies of one's opponents is essential to winning. A "Nash equilibrium" is a situation in which each player's strategy is an optimal response to the play strategies of the other players. There is no room for "selfishness" or George-Bush-style "go-it-alone" bravado here. While tolerance and intolerance are not exact a "game," the principles of Game Theory can be applied in a broad way to understanding why tolerance is the superior of the two principles. If you tolerate the opinions of those you disagree with, the chances are greater that they will tolerate your opinions. And if everyone held to the principle of tolerance, then we wouldn't even need to worry about chances being greater or less: we would know right off the bat that others will indeed tolerate our opinions. In this climate of tolerance, there would be a lower risk of conflict, and instead of expending our energy fighting each other, we could put it to more productive ends.
What the paradox of tolerance teaches us is that rationality is not always in lock step with practicality. The rational thing to do is not always the best thing to do, the most practical thing to do, the right thing to do. I am not speaking here of the morally right thing to do, but rather, the right thing in terms of common sense. It should be noted that common sense is not always rational. Philosophers often dismiss common sense precisely because of this. But if common sense had prevailed, world history might have run a very different course.
So what shall we say of tolerance? Should we be rational and reject it as a guiding principle because it is self-contradictory and therefore illogical? Or should we yield to the irrational side of our natures and embrace tolerance despite the fact that it is self-contradictory and illogical? I think most people would agree that the latter is the more "sane" of the two options.