When people call themselves sunni, they are asserting that they follow the sunnah of the Prophet. Sunnah means the teachings, deeds and sayings of the Prophet Muhammad. When people call themselves shia, they are asserting that they are the followers of Ali because the word 'shia' means follower. Sunnis and shias are both Muslims, but there is nothing wrong with calling ourselves 'The followers of Ali' or 'The followers of the teachings of the Prophet'. Following Ali and following the teachings of the Prophet are extremely important, do you not agree?
You're problem here is that the sunni-shia sects are causing a division in Islam. While that may be true, but what other way can we differentiate our beliefs and school of thoughts if we didn't have sects? Sects determine which school of thought we follow. Shias follow the jafari school of thought, in other words the ahlulbait (the Prophet and his family) school of thought. Sunnis follow the one of the 4 imams school of thought (hanbali, shafi, maliki, hanafi). If we only referred ourselves to Muslims, how can one find the truth?