Lil:
The average nursing home has about a hundred residents.
Figure that in the course of a week some one visits most of them.
Then you have an on-site staff of at least a dozen folks, who in turn are exposed to their own family members and the general public.
Then you have vendors that show up to deliver a wide variety of supplies.
All it takes is one asymptomatic positive person to enter the facility and you have a disaster.
Also, many nursing homes have wings for short-term rehabilitation (often adults of all ages). These are people who were just released from a hospital—which as we know is the very easiest place to catch the virus.