1. Vaccinating people who are the most likely to get sick
2. Vaccinating people who are the most likely to spread the virus
Option 1 makes the death and hospitalization rates fall quicker, so that anyone we miss is more likely to still have a hospital bed to get treated in. Option 2 reduces the total number of people exposed to the virus.
The whole point of vaccination is to keep people from having to go to the hospital or dying - protecting the weakest first achieves that better than random vaccinations. Someone like me who basically lives in his room and works remotely can afford to wait for shots - someone who works in retail and has 1000s of exposures per day needs their shots yesterday.