What is the ruling on a Muslim feeling arrogant towards a disbeliever, while also feeling ashamed for not inviting him to Islam?

A Muslim should feel honor in his religion, not arrogance, for he is not deluded about his faith, which is the most perfect of religions. A Muslim's feeling that he is upon the truth, and that non-Muslims are astray, is a correct belief that obligates him to show humility to Allah and thank Him for His guidance. Furthermore, inviting people to Islam is a fundamental characteristic of this Ummah, so a Muslim should seize opportunities to invite non-Muslims after arming himself with religious knowledge. If he cannot engage in da'wah himself, then the least he can do is to assist those who can.