Correction: the 9th of 'Av this year equals the night of 7/23 and the day of 7/24.
I guess you missed my clarification a few replies later. It's just automatic for most westerners, even those familiar enough not to make the mistake of equating date for date, even though they overlap. Try not to get too frustrated, lol. It once sounded strange to me, the concept of having days begin at sunset, but then I began to wonder at the logic of having days begin in the middle of the night, as we do.
If pure logic had anything to do with it, the day's date would begin with sunrise.