Certainly such definitions if taken objectively would bring no offense, but say such a word to someone in a derogatory fashion, and the intent of insult could hardly be missed. Such was the intention of the Romans who perceived the disciples of Jesus Christ as objects of curiosity, or even monstrosities, and at the very least, enigmatic followers of a strange religion.
However they couldn't deny how these people loved one another, or the One that they claimed to be the Son of God, only begotten of God. In a derogatory manner, the Romans referred to this strange lot of people as "little Christs", a term meant to ridicule and insult.
Yet when the disciples heard of it, they were humbled by such praise, as to even be compared to the LORD of Glory whom they served with love and obedience. They were first called "Christians" in the city of Antioch. Christians today are similarly confronted with another derogatory term, "Jesus Freak" and take exception to such words, for as we look upon our past and compare it with the life we now have with Jesus, we would readily agree that we WERE once freaks, but are now as God intended us, redeemed by the Blood of the Lamb and indwelt by the Spirit of the LORD.