Midnight meal, baby! A 1AM meal isn’t breakfast, it’s drunk food! Praise the chow hall for being open at that time!
24:00 is used in military log books because they are normally kept to the minute, not the second. Often the change of day is logged to make it easier to find dates when rereading the log. So the typical entry might be 00:01 (date) a new day, or something to that effect.
Part of the reason might also be that if you advertise a boat as being at, say, 00:00 on Wednesday, you might get people turning up on Wednesday night, i.e. nearly 24 hours late.
Saying it is 23:59 on Tuesday instead removes the ambiguity.
It’s the same reason that competition closing dates are often given as “11.59pm on August 31” or whatever. Some say “midnight on <date>” but I always think that’s ambiguous – I would assume it meant the end of that given day, but then 00:00 is shown on clocks as being part of the next day, as mentioned above. (But that is simply because if a clock shows “00:00:00” then by definition it is after midnight, as the display doesn’t tick over until the exact moment passes.)