Why might a master free a slave?

The most usual reason for a master to free a slave would be as a reward for the good work that had been done by the slave. Masters are not required to reward their slaves, but they still may be generous enough to do so. There are also a number of cases in which slaves inherit their freedom when their owner dies, on the principle that it is enough for the slave to have served the master for the master's entire lifetime, without having to also then become the slave of the master's heir. Again, that is not required, but it is a reasonable act of kindness that costs the master nothing.