There are a couple of reasons for this villager's behavior. One of them is that the villager cannot find its path to the workstation block. Additionally, villagers work only during the work time during the day. That means early in the morning and late in the evening, they won't try to work and won't be assigned a new profession. One more reason can be the fact that some other villager is occupying that job site block, so the villager you want to assign the job cannot take it. Try to isolate all the other villagers outside of the room and the chosen villager will soon take that job if it's middle of the day.