It is alleged that Islam divides mankind into Believers and Infidels/Kafirs;
Kafir means one who rejects or denies.
Kafir is derived from the word Kufr, which means to conceal or to reject or to deny.
Kafir is the one who conceals or rejects or denies. This is contrary to how some people wrongly translate Kafir as Infidel.
Kufr is not a curse or an insult. A Muslim also has to do Kufr, not with Allah but with all that is worshipped other than, or along with Allah.
“Whoever disbelieves in taghoot (yakfur bialtaghooti) and believes in Allah alone, then he has grasped the most trustworthy handhold that will never break” The Holy Quran, Chapter 2, Verse 256.
So a Muslim also has to do Kufr, He has to be a Kafir of Taghoot. Taghoot means all that is worshipped other than, or along with, Allah. If Kafir was an insulting word, Allah would not have used it for Muslims.
In general Kafir is a term used for a person who rejects Islam. However if a Non-Muslim considers being called a Kafir as an abuse, it is due to his/her misunderstanding about Islam. He or she needs to reach out to proper sources of understanding Islam and Islamic terminology, and not only will he feel abused, but rather appreciates Islam in the proper perspective.