By the way the phrase "first moves for the purpose of taking off" is usually interperted as when it first taxis with the intension of taking flight, but it could of course be read differently.
My two cents...
"for the purpose of taking off" means I'm taxiing out with the full intent of taking off once I reach the runway. That intention may change due to a technical problem or weather or anything else, but that doesn't make the time any less loggable. So it can go into the logbook, although obviously with zero take-offs and landings. And you might want to write in the comments why the flight was aborted.
In my view the legislators wrote the phrase "for the purpose of taking off" to contrast it with "for the purpose of taxiing to the pumps/hangar/maintenance bay/sightseeing across the airfield/whatever", which clearly is not loggable.