I know it's because I have a tendency to over-think/complicate things sometimes. I'll give you a sample conversation.
Me: Remind me. What time is the plumber coming tomorrow?
Ross: Half Ten.
Me: (thinking, not aloud) Wait. Does that mean 9:30 or 10:30? I think it's 9:30. Right? Because it's half way to 10. Right? Wait. Half ten would be 5:00 so that can't be right. (out loud) ...10:30?
This repeatedly confused me for WAY longer than I should admit. I know now what it means. And only second guess myself very infrequently. But it's definitely an interesting difference. I've never heard a British person say "thirty" as part of the time. It's always "half". I wonder why that is...