Angle down means that the point is thrust away from the grinding wheel should any sort of hang up, or grossly excessive feed, occur.
Angle up means that any hang up tends to pull the point into the wheel further increasing the stress on it.
Given the inherent brittleness of grinding wheels such increase in stress is generally considered a bad thing as it could lead to the wheel shedding pieces or even exploding. Neither being a pleasant prospect when standing close by. Best grinding practice requires you to be aware of any chance of over stressing the wheel in any way and arranging things to minimise any chances of such things happening.
Quite a few old time practices are safe only when the wheel is driven by a lightly tensioned belt drive so anything approaching a hang up stalls the wheel. Something to be aware of when scouring historical works. Modern direct off the motor drives are unforgiving. Doesn’t help that most double ended grinders are objectively significantly over-powered for pure grinding duties as the makers, rightly, assume that they may well be used to drive wire wheels or polishing mops which do need the power. Its important to use wheels designed for double ended grinders as these are more robust than those intended purely for tool grinding.
One thing that worries me about amateur designed drill sharpeners and similar fixtures is that the drill, or other tool, is invariably held rigidly. My Clarkson drill sharpening attachment has a spring loaded pin pushing the spindle out against an internal stop. This allows about 1/8″, 3 mm, push back if you overload things. Not a perfect safety measure but it does help. Yes I have been grateful for that in a couple of brain fade moments when inadvertently dialing in too much feed. Subsequently I realised my initial set up procedure was bad leaving openings for such errors. So i changed my methods, hopefully closing the loopholes.
Geometrically point down should be easier to make stable but I doubt if the forces involved in grinding are sufficient to make brute stability an issue. Damping against vibration is the main reason why grinders tend to be big and heavy.
Clive