"That's just how my family talks"
Some readers will have a ready answer, which is that in their family everyone talks over everyone, and always has, and it's warm, and nobody's harmed.
I think that's partly true, and I want to separate the two things inside it.
There's a kind of overlap that doesn't take the turn. "Yes, yes, exactly." Laughing before the punchline. Saying the last word along with the speaker. Two people finishing a shared story at once. In that kind, the first speaker keeps talking, or finishes, and the overlap is a sort of accompaniment. Many families and many friendships run at this tempo and it's a pleasure to be in. Stivers's ten languages differed in their average gap by up to a quarter of a second, and that's enough, the researchers thought, for one culture to feel another as rudely fast or painfully slow. A fast family is a real thing.
Then there's the overlap that takes the turn. You start, they stop. The story ends with your version. That's the jump, and the test for which kind you're doing is simple. Who's talking afterwards? If they're still going, it was accompaniment. If it's you, it was a jump, however warm it felt.
Most people who grew up in a fast family do both and can't tell them apart from the inside, because both feel like joining in. The tally will tell you. Count only the ones where you ended up with the turn.
The other thing to say about the family style is that it doesn't travel. At your parents' table, the jump might land as warmth, because everyone there is doing it and the turn comes back round. With your partner, who grew up with gaps, it lands as being cut off. With Priya, it lands as being overruled. The style isn't wrong. It's local. And most of your conversations aren't at that table.