Yes it is! Quran is the word of almighty Allah (swt) as a guidance to the whole mankind, it is a way of life. It is the duty of every muslim to invite his/her fellow beings towards the truth.
As the Quran says: 'Invite (all) to the way of thy Lord with wisdom and beautiful preaching; and argue with them in ways that are best and most gracious.' [Al-Qur'an 16:125]
Now its the will of the kafir whether he converts or not, there is no compulsion as stated in Quran:
'Let there be no compulsion in religion: Truth stands out clear from error' [Al-Qur'an 2:256]
And yes u r true, every muslim's life has to begin and end at Qur'an. Islam means 'submitting ones will to Allah (swt)' and how can you do that by differing from the woed of Allah (swt) i.e. the Quran?!!
