How would that be "totally incorrect"? There are only 24 hours in a day. It's incorrect to claim that there's 25, 26 or 27 hours in the day - even if it's useful and proper, it's not technically correct.
I'm making a guess here, but I think he means specifically the (A) "arrives every weekday at 00:37" part. That has a different implied meaning than (B) "the train arrives every weekday at 24:37." (A) implies that it will arrive every Monday through Friday mornings at 00:37 but will not arrive on Saturday or Sunday mornings at 00:37. (B) implies that it will arrive Tuesday through Saturday mornings at 00:37, but not Sunday or Monday mornings.
In the context of the train departure time, it's easy to work out what is meant by a weekday 00:37 arrival, but if they were divorced from each other for some reason, weekdays at 24:37 would be easier to interpret.
right - 24:37 friday makes is read as "37 past midnight on friday night" - which is friday night as humans consume time, but saturday morning by the calendar.
Being awake past midnight brings up a few challenges with calendars. My watch wil count a late (late) night walk against tomorrow, not against today. As a human, I consider "tomorrow" as "after I've gone to sleep", not "after midnight". 00:37 is still very much tonight.
An app I have to track habits and streaks lets you specify the time to count as "that day". I often walk my dog after midnight, so I have this set to 3am.
Think of it as a 24 hour day that starts at (to use UK public transport's setup) 4:30. You want the timetable and the users to agree on what 8am means, and that 8am and the following 2am are the same work day of 24 hours.
In the context of the train departure time, it's easy to work out what is meant by a weekday 00:37 arrival, but if they were divorced from each other for some reason, weekdays at 24:37 would be easier to interpret.