(Exodus 22:1) introduces the law of the burglar: "If the thief be found breaking in." The Mekhilta clarifies what the homeowner's mental state must be. The verse describes a situation of doubt in the owner's mind — not certainty, but reasonable uncertainty.
The doubt is: did the burglar break in to steal, or to kill? If the homeowner faces someone who might be a murderer, the homeowner is permitted to kill the intruder in self-defense. This is the Torah's foundational statement on defensive force.
But the Mekhilta considers an alternative reading: perhaps the doubt is whether the intruder came to steal or had no criminal intent at all. This reading is immediately rejected through an a fortiori argument. If the intruder definitely came to steal and the homeowner killed him, the homeowner would be liable for murder — you cannot kill someone just for stealing. If that is true for a certain thief, it is even more true for someone who might not be stealing at all.
The only reading that works is the first one: the doubt is between theft and murder. The homeowner sees an intruder breaking in at night and cannot determine whether this person has come merely to take property or to take a life. In that moment of genuine uncertainty, the Torah permits lethal self-defense. The doubt about the intruder's lethal intent is what creates the legal permission to use deadly force.