Did you not read the actual linked article on Self Defense… ?
How extensive is a man’s right of self-defense of person and property? The basic answer must be: up to the point at which he begins to infringe on the property rights of someone else. For, in that case, his “defense” would in itself constitute a criminal invasion of the just property of some other man, which the latter could properly defend himself against.
…
Defensive violence, therefore, must be confined to resisting invasive acts against person or property. But such invasion may include two corollaries to actual physical aggression: intimidation, or a direct threat of physical violence; and fraud, which involves the appropriation of someone else’s property without his consent, and is therefore “implicit theft.”
Thus, suppose someone approaches you on the street, whips out a gun, and demands your wallet. He might not have molested you physically during this encounter, but he has extracted money from you on the basis of a direct, overt threat that he would shoot you if you disobeyed his commands. He has used the threat of invasion to obtain your obedience to his commands, and this is equivalent to the invasion itself.
It is important to insist, however, that the threat of aggression be palpable, immediate, and direct; in short, that it be embodied in the initiation of an overt act. Any remote or indirect criterion – any “risk” or “threat” – is simply an excuse for invasive action by the supposed “defender” against the alleged “threat.” One of the major arguments, for example, for the prohibition of alcohol in the 1920s was that the imbibing of alcohol increased the likelihood of (unspecified) people committing various crimes; therefore, prohibition was held to be a “defensive” act in defense of person and property. In fact, of course, it was brutally invasive of the rights of person and property, of the right to buy, sell, and use alcoholic beverages.
…
It should be clear that no man, in an attempt to exercise his right of self-defense, may coerce anyone else into defending him. For that would mean that the defender himself would be a criminal invader of the rights of others. Thus, if A is aggressing against B, B may not use force to compel C to join in defending him, for then B would be just as much a criminal aggressor against C.
Here is a way better one, (i.e more difficult case - in yours, there are no injuries or damages to the victim, here - there will be) but I could possibly take the time to address yours, if you still don’t get it.
Jonah Goldberg and the Libertarian Axiom on Non-Aggression
…
You are standing in the path on an onrushing boulder, completely unaware of your fate. In a second, this massive rock will hit you, and you will die. (Let us stipulate the truth of this supposition). Instead, however, I push you out of its path, and into safety. The only trouble is, as a result of it, although I have saved your life, I also broke your arm.
Now, if you are a reasonable sort of person, you will be grateful to me. Instead, you insist upon sticking to the literal letter of libertarian law, and sue me for damages for the injury you have sustained. After all, I did initiate a violent act upon your person, which resulted in an injury. If this is not assault and battery, you argue, then nothing is. How shall the libertarian judge rule?
One possibility is to hold me innocent of this charge. This could be done by adding up the two acts, the life saving and the arm breaking, and deciding that the former is far more important than the latter. So much so that the one ought to be in effect “subtracted” from the other, and since the result would be a “positive” (I contributed more to your life by saving it than I cost you through the injury you sustained), I would be let off scott free. The point here is that I committed not two acts, but only one: saving-your-life-and-injuring-you, and that this complex but single act is not one of initiatory aggression.
A difficulty with this line of reasoning is that you might have been standing in the way of the boulder as part of a suicide attempt. You regarded the situation where you are dead far more highly than the one where you are alive, but debilitated. We may assume you wanted to end your life because of bodily malfunctions like a broken arm, and now I have worsened your welfare, not improved it.
Another problem is that these really are two separate acts. It is certainly possible that I could have pushed you out of death’s way without breaking your arm. To call it two separate acts is really to fudge: this would only be done in order to achieve the common sense result we all presumably want: to find me innocent of bodily harm.
No, the only proper libertarian judgment is that I am indeed guilty of a battery upon your person. My motives may have been exemplary, but my act, strictly speaking, was in violation of your property rights in yourself. I might well be let off with a light sentence, given the extenuating circumstances, but guilty I am. …