The confusion is cased by the fact that different groups define the term Christian differently. A Catholic would define a Christian as anyone who professes faith in Christ and who has been validly baptized (water baptism).
Many Protestants do not use the term Christian in this way. Different denominations have different criteria for determining who is a Christian—e.g., Christians are those who have "accepted Jesus Christ as their personal Lord and Savior" or those who profess to be saved "by faith alone." Since Catholics don’t generally use this language, they classify Catholics as non-Christians (though many are willing to concede that some Catholics are Christians even though they don’t use this language).
For those who approach you with this issue, point out several things to them: (1) Catholics are Christians; (2) the Catholic Church is the Church Jesus started and which he said would never pass away (Mt 16:18); (3) when Scripture speaks of Christians it speaks of every church member as a Christian, no matter what his "walk with God" may be like; and (4) Christians throughout history have always recognized baptism as the method by which one becomes a Christian. It was not until after the Protestant Reformation was underway that people denied this.