Why is low sprocket minimum 28t for a Shimano 105-GS? I have a Shimano 105 R7000 GS (medium cage) rear derailleur and would like to mount a 12-25 cassette. According to its specs, this should not be possible.

I am just wondering: why not? A GS-cage will manage a 25t sprocket fine in many cassette combinations and in reality go as low as 11t. I understand, there is a problem in the other direction and a max on how many teeth it can handle on the highest sprocket. 

Would anyone know, why a GS derailleur cannot handle a 12-25 cassette?

Thanks
Morten
The key aspect of the GS cage is the length of the cage. The other key aspect of   derailleurs is the geometry of the parallelogram.

Because the design has been adapted to suit more modern gearing with larger max sprockets, it moves downwards at a steeper angle, with room to accommodate the larger cogs. Therefore if a tighter range cassette is fitted, the guide pulley is now further away from the largest cassette than older GS derailleurs on the same cassette.

This is going to reduce the accuracy of the shifting a little if you can't move the guide pulley up enough using the b-tension screw. In practice of course, Shimano are famously conservative and breaching the spec might not give any issues. The 12-28 cassette is guaranteed to work, the 12-25 is not.