When you use the Tor Browser, the home page tells you that you are connected
to the Tor network and are using a specific IP address. Many times when I use
Tor, I get curious and do an IP lookup and it tells me the the country and
state (if in the US) of the IP I am "borrowing" for that session. That is how
I could watch streaming video on the BBC iPlayer by forcing my exit nodes to
be under the UK.
Tor is "private" in the sense that you browse the internet under an IP
different than yours. If you were to run an exit node and a handful of people
were using your IP to upload and discuss child pornography, how would you be
able to prove it wasn't yours? It is an IP assigned by your ISP that is tied
to your account with your personal information.
At the end of the day, the sites you visit under that "borrowed" IP address
may keep a record of that IP's visit and if they were forced to share
visitors with the government for any reason, they tie that IP to the activity
at that time. The user that was providing the exit node now has this activity
tied to his IP address that he or she may not be aware of and is taking a
HUGE risk by sharing it.
I can't moderate what someone would be doing with my IP address and sure
would not want to serve prison time either due to the logged activity. That
is why I would never run an exit node in Tor.