Why Churches of Christ?

I was asked by a Catholic with this question:

In the Romans 16:16 it was mentioned "churches of christ". Does it mean that there are lots of churches of christ?

Actually, what was referred to when mentioned "churches of Christ" was the members of the church. The members were called "churches of Christ" because the church of which they were members was the Church of Christ.

For example: why are we calling some Christians as Catholics? Well, it's because they are member of the Roman Catholic church.