Well 50% of what?
If it's your life expectancy that's something most people never know for sure, and so much of the time an estimate for that can be inaccurate by decades, therefore the 50% point would by inaccurate by half as many decades.
Same goes when you look at it like about half your useful lifetime, or your adult lifetime, perhaps your professional longevity, these are all different things but overall life expectancy still figures in.
OTOH I think middle age has a "feeling" all its own and it might be less inaccurate [0] to try and pinpoint when that gets underway. Which I think people have good ideas about and the way it's commonly considered to "creep up on you" does indicate another reason why it's difficult to perceive exactly, since we are all like frogs gradually warming up to a boil ourselves at the same time trying to get an idea when we're halfway cooked :)
Now the middle-age slowdown has been cited as a marker for centuries so there must be something to it.
I would say when you feel you're about halfway to what you would like to accomplish, which is often quite remarkable in itself at the halfway point, and you take that opportunity to slow down or halt, even with well-deserved rest upon your laurels, that would be the time middle age starts without question.
[0] Better, but not quite as good as "more accurate" ;)