At first I want to say that, Allah says before praying you should do wudhu but he does not want to put you in hardship .as he says in Quran:
O you who believe, when you rise up to prayer, wash your faces and your hands as far as the elbows, and wipe your heads and your feet to the ankles. Qur'an, 5:6
All the Muslims had a same manner of performing Wudhu until the third khalif and it was the same manner of Shia, but he (third khalif ) in his middle years of Caliphate , was plagued by doubts when he compared his manner with the prophet . Then he changed the manner of performing wudhu to the way that is common in Sunny people and announced:
“Clean hands from fingertips to elbow” and insist on the “washing of the feet and not the anointed.
This heresy, opposed many of the companions of the Prophet ( pbuh ) , but the Umayyad because of their politic purposes Propound this manner in different parts of Islamic countries and made such atmosphere that no one could show his disagreement . So this manner was propagated.
Fars news agency