Air rifles are often used for hunting small game: squirrels, birds, rabbit, etc. Some of the high-end higher caliber air rifles are used to hunt game as large as hogs. So an air rifle can be used with lethal force. That said, a human assailant is not small game. A determined assailant might not be stopped by the average hunting air rifle. But if it is all you have, it may be sufficient.
At this point, let me emphasize: I’m not a lawyer, and this post contains no legal advice. It may or may not be legal for you to use an air rifle in self-defense. Check your local and national laws, and obey them. A few states and localities have some general restrictions on air guns. Laws vary from one nation to another. In the U.S., there are few restrictions on air guns. By contrast, in the U.K., air guns are highly regulated and are limited in muzzle energy (unless you have a special permit?).
Every now and then, a gun self-defense story hits the news media. The usual situation is that the bad guys run away, as soon as they see a gun, or as soon as the gun is fired. Very often, when a gun is used in self-defense, no one dies. The bad guys don’t stand their ground and shoot it out. They run.
Sometimes the person using a gun in self-defense is an adolescent with maybe a .22LR rifle, even a bolt action. That’s not much gun to fight off an adult assailant. And yet the bad guys just have to see the gun, or hear it fire once, and they take off running.
My point here is that any gun is better than no gun. Even an air rifle may scare off an assailant, who may not realize it is only an air rifle. A scoped break-action air rifle gives you one shot only. But it looks a lot like a regular firearm. Brandishing the rifle when faced with a deadly threat may be sufficient. The high-end PCP air rifles (pre-charged pneumatic) are multi-shot, usually by working a side lever. So you at least can do a follow-up shot or a double-tap. But a PCP rifle is a lot more expensive than a break-action air rifle.
Can an air rifle kill? Just wounding an assailant may be sufficient to stop the threat. But if it is not, an air rifle that is sufficient to kill small game can be used with deadly force, if the shot is well-aimed (head or heart).
The most common calibers for air rifles are: .17, .22, and .25. As you might expect, the low-end .17 has the least power, and is not ideal even for small game. The .22 is the most common caliber for small game hunting, but .25 caliber has much more power. Some exotic and expensive air rifles are available in .30, .45, and .50 calibers. But at that point you might as well just buy a firearm. So for self-defense purposes, stick with .22 or .25.
Interestingly, most air rifles come equipped with a “moderator”, which greatly reduces sound. An air rifle is about as noisy as a common staple gun. Loud enough to get the attention of the assailant, but not loud enough to require hearing protection. Almost all air rifles come with moderators, which keep the sound level down.
An air rifle is also a great first gun for a young shooter. Before you introduce your kid to firearms, you might start with an air gun. Kids can learn firearms safety just as well on the air rifle. And the low noise and practical absence of recoil is a plus, too.