I totally agree and I don't have any problem with this.

23:55 = one day
00:05 = the following day.

Is the lack of standardisation an American thing?

I've never had a problem looking on web sites run by Air New Zealand, Qantas, Emirates, Singapore Air, Thai Airways, LAN, KLM, and several others. They all list the 00:05 flight as departing on a new day, not on the evening of the previous day.

And talk of 26-hour days (as one poster suggested) is just plain nuts!