Muslim comes from the word Islaam in the arabic language, and because Islaam is a verb (doing word), to do Islaam is to be in a state of 'submission.' So we have to find out what Islaam actually means.
The Meaning of Islam
"ISLAM" is derived from the Arabic root
salaama peace, purity, submission and obedience. In the religious sense, Islam means submission to the will of God and obedience to His law.
Everything and every phenomenon in the world, other than man and jinn is administered
totally by God-made laws,they are obedient to God and submissive to His laws, i.e. they are in the
state of Islam. Man possesses the quality of intelligence and choice, thus he is invited to submit to the good will of God and obey His law, i.e. become a
Muslim. Submission to the good will of God, together with obedience to His beneficial law, i.e. becoming a Muslim, is the best safeguard for man's peace and harmony.
Islam dates back to the age of Adam and its message has been conveyed to man by God's Prophets and Messengers including Abraham, Moses, Jesus and Muhammad. Islam's message has been restored and enforced in the last stage of the religious evolution by God's last Prophet and Messenger Muhammad.
The word
ALLAH in the Arabic language means God, or more accurately The One and Only Eternal God, Creator of the Universe, Lord of all lords, King of all kings, Most Compassionate, Most Merciful. The word Allah to mean God is also used by Arabic speaking Jews and Christians.
more info:
http://www.usc.edu/dept/MSA/fundamentals/pillars/intropillars.html
If you can explain them concepts clearly, then the point on Jesus son of Mary (peace be upon them) being Muslims isn't hard to accept. Infact it's much more logical since christians themselves believe that the previous Prophets of Allaah were humans and submitted to what Allaah/God revealed to them, and Jesus son of Mary was also an honorable Prophet of God and we believe that he also recieved a divine revelation from Allaah/God [the Injeel/Gospel.] And Muhammad (peace be upon him) is Allaah's final Messenger since he came with the same message of all the previous prophets [of the worship of God/Allaah Alone] - while other things were abrogated [removed from the previous Shari'a/laws etc.]