How do I explain a career gap without sounding defensive?

You have got an answer ready, but you can feel it come out braced and tight, and the tension is what lands badly, not the gap itself. When you defend, you signal there is something to defend. The fix is less about better words and more about a calmer stance. Treat the gap as a plain fact, because it is one. You took time off, or lost a job, or life happened. Say it briefly, without apology or over-explanation, then move to what you offer now. The shorter and steadier you are, the smaller it looks to them. One small step: write your explanation in two calm sentences and say them aloud until they sound like you are stating the weather. Practice drains the fear that makes it come out defensive.