1. Because Hindu word does not origin from any reliable Hindu text.
2. Because the word Hindu has a disputed origin and historically used by foreigners to abuse us. In Persian dictionary, it means, “black, thief, rascal” etc.
3. Because we consider our culture to be the oldest one. So we can always get a better word to name ourselves which is neither disputed and nor borrowed from foreign dictionaries.
4. Because even if we agree that popular perception of “Hindu is not what the meaning in Persian dictionary is”, the question remains that Is my culture so lacking in content that I have to adjust with such dubious names to identify myself?Is compromise a destiny for our society?If we can compromise even on our name, how can we ensure that we will not compromise on other issues that threaten our culture?
5. Because I believe that Vedas provide better alternatives to Hindu. We consider Vedas to be divine, and hence these names with noble meanings would be better ways to call ourselves. An example is Arya.
6. Because if we agree that Hindu is not our ancient name, but still should be continued for sake of convenience, then it means that there is nothing eternal or permanent about the word Hindu. If we can transform from Arya to Hindu, then what shall prevent us from getting changed into say, lafanga (Persian meaning of Hindu) tomorrow?And when that transformation is bound to happen as per historical data, why should not I proactively decide to change my name to my liking rather than wait for tragedies of tomorrow to decide our name?Is this lack of proactivity a destiny for our society?
7. Because historically we have always called ourselves Arya. It was advent of foreigners, which popularized the word Hindu. Neither did Ram call himself Hindu nor Krishna. Even Chanakya did not use the tag Hindu. It were the Muslims who popularized this adjective to denigrate us. And after 800 years of misrule, when British came, they chose to tag us as Hindus for census purpose.
8. Say China starts calling us Bastards, and then by fate of destiny, they rule over us for some years. Then perhaps I may start yelling, “I am proud to be a Bastard!”. The story is same in case of Hindu, except that instead of China, we have Britain and Muslims, instead of Bastard, we have Hindu.
9. Because some experts claim that Hindu word came from Sanskrit word Indu. If that be so, let us start calling ourselves Indu rather than Hindu. And in that case, why not simply call ourselves Indian. Because India too has same root!
10. Because language changes over centuries. So even pronunciations and names may change. But in case of Hindu, it is not change of pronunciation that forced change of our name. It is instead representative of a dark era of slavery of barbaric gangs, that forced us to admit the abuse hurled on us as our name of pride forever!
11. Because nothing is bigger than dignity. And my name is first sign of my dignity.
12. Because I am proud of belong to a heritage that is oldest  is world and full of such high ideals and science that inspires the entire world since dawn of civilization. Let my name be a symbol of that eternal benevolence. Let we call ourselves Arya!

Further references:

http://www.stephen-knapp.com/about_the_name_Hindu.htm

Meaning of Hindu