Catholics are Christians. In fact, we are the very first Christians. And we who call ourselves Catholic are no less Christian than Lutherans who call themselves Lutherans, or Methodists who call themselves Methodist, etc.
A primary argument is historical. The Protestant denominations are all less than 500 years old in terms of their founding. The human founders of these denominations such as Martin Luther, John Calvin, et al., broke away from Catholicism and/or each other. Further, their existence is a relatively recent historical phenomenon in the more than 2,000 years of Christian history.
The Catholic Church, which include Roman (Latin-rite) Catholics and Eastern-rite Catholics were not founded by mere human beings, but by the Lord Jesus Christ, and built on the rock of St. Peter.
In Acts 11:26, we are told, “It was in Antioch that the disciples were first called Christians.” This declaration and description was made of the Church more than 1,500 years before any Protestant denominations ever existed.
Hence, the Catholic Church has borne the title “Christian” long before any breakaway groups ever used the term to describe themselves.
We do not deny they are Christians and neither should they deny that of us, for the reasons stated. Catholics are Christians to be sure, the first Christians.