I have seen so many Arabs who really are proud on their blood and treat non-Arabs cheap. Sometimes they can be arrogant. When you question them they say "I am Arab you are non-Arab". It really ticks me off. When I asked the Imam who is non-Arab, he said you should not say anything wrong to them because Prophet Muhammad was one of them and we respect them because of Prophet Muhammad. Is there any justification for Arabs to be rude?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Islam, which is the only true religion, does not establish any preference for Arabs over Non-Arabs. The preference in Islam is determined by the righteousness the piety and the good deeds. Allah Says (Interpretation of meaning): ": {Verily, the most honourable of you with Allah is that (believer) who has At-Taqwa (God fear)} [49: 13]. The prophet says: "There is no preference of an Arab over a Non-Arab except by the (degree) of piety."(Imam Ahmad) So the best people for Allah are the most righteous ones. The status of each person is determined according to the degree of piety he has reached. Indeed the believers are brothers as Allah Says (Interpretation of meaning): "The believers are nothing else than brothers"(49:10) They support and protect one another as Allah says; (The believers men and women, are Auliya (helpers, supporters, friends) [9:71]
Help, protection, and support require love, compassion and good advice regardless of the colour the ethnic group or the sex. In fact, raising such issues (colour...) and putting forward such ideas is against Islam and causes much harm to the unity of the Muslim world. No doubt that Muslims are in dire need nowadays for this unity in order to overcome the problems and challenges that are facing them. Finally I would like to point out two very important things for the people you described in your question; Firstly, Jabir said: "We were in a Ghazwa (Sufyan once said, in an army) and a man from the emigrants kicked an Ansari man (on the buttocks with his foot). The Ansari man said, "O the Ansar! (Help!)" and the emigrant said, "O the emigrants! (Help!)" Allah's Apostle heard that and said, "What is this call for, which is characteristic of the period of ignorance?" They said, "O Allah's Apostle! A man from the emigrants kicked one of the Ansar (on the buttocks with his foot)." Allah's Apostle said, "Leave it (that call) as is a detestable thing." It is clear from this Hadeeth that such behavior is very bad and harmful for Islam and Muslims. This is why the hypocrite Abdulla Ibn Oubey took the opportunity of what happened between the two men mentioned in the Hadeeth and said; "If we return to Al Madina, indeed the more honourable will expel therefrom the meaner." Secondly, know that most Muslim scholars are non-Arabs; (ALBUKHARI, SIBAWAIHI, ABU HANIFA, five of the prominent seven Imams in the sciences of the Qur'an...etc.) So non-Arabs should not be overlooked by any Arab who believes in Islam. As for how to deal with such people, we advise you to be patient with them and advice in the best way. But if they keep on behaving in such a bad way do what Allah says; "And turn away from the foolish."(7:199) And Allah knows best.