Make sure you have enough permission for cassandra user and cassandra group. I would prefer cassandra to have control over its own directory, along with the data directory and log directory since I used the default system.log location.
For my cluster, I used:
chown -R cassandra:cassandra /opt/cassandra/
chown -R cassandra:cassandra /var/log/cassandra/
chown -R cassandra:cassandra /var/lib/cassandra/
And then you can check for system output files in the above locations for error if you have any.