Because of the many hadiths they have regarding this matter, the Shia pray with open hands in order to have followed the tradition of the holy prophet (pbuh) and the imams (as). These hadiths express that the prophet (pbuh) and the imams (as) would pray with their hands open and at their sides, and that praying with closed hands resembles the Maji. Also, there are reliable hadiths that explain how the prophet's (pbuh) prayer was from start to finish, yet there is no sign of him closing his hands during the prayer in them. Anyways, the closing of the hands was something coined after the prophet's demise, during the caliphate of the second khalifah, and that is the reason why the Sunnis pray with closed hands; although some of them still don't practice such an act.
Praying with closed hands is a method that didn't exist during the prophet's time, because the prophet (pbuh) himself would pray with open hands, and since the Shia solely believe in following the prophet (pbuh) and the imams (as) in all fields, they also pray with open hands, and regard praying with closed hands as bid'ah or forbidden innovation. This method of praying was innovated during the second khalifah's rule, became the formal prayer style then, and was continued till today, to the extent that most Sunnis still pray the way the second khalifah had ordered in his time. But the imams (as) have said that this method resembles that of the kafirs and the Maji and have asked their followers to pray with open hands; the same way the prophet (pbuh) would pray.
Abi Hamid Sae'di has described the prophet's (pbuh) prayer in a hadith in full detail, from the beginning of the tahbiratul-ihram till the end of the salam, yet hasn't mentioned anything about him closing his hands, and instead says that after saying the takbiratul-ihram, he brought his hands down by his sides.
At the same time, one can't say that closing the hands isn't obligatory in the prayer and is only mustahahb, and that is why the prophet (pbuh) wouldn't close them, because it is impossible for him not to perform this "mustahabb" act all his life.
In yet another hadith, Hammad ibn Isa asks Imam Sadiq (as) to portray the full and correct prayer for him. The imam (as) stood towards the Qiblah, observing all of the mustahabb acts, said the takbiratul-ihram and began reciting and went on to finish the prayer the way the Shia currently pray, ending it with the salam. In this hadith, the imam (as) was showing Hammad how the prophet (pbuh) would pray, yet there is no sign of the closing of the hands, and if this act was to truly be a tradition of the prophet, he would have surely included it in his description of the prophet's (pbuh) prayer.
There are also multiple hadiths by the imams that say this act resembles that of the Maji and the kafirs and one shouldn't practice it; here we will list a few:
a)روی محمد بن مسلم ،عن الصادق (ع) او الباقر (ع) قال: قلت له: الرجل یضع یده فی الصلاة -و حکی- الیمنی علی الیسری؟ فقال: ذلک التکفیر لا یفعل. 
b)روی زراره عن ابی جعفر (ع) انه قال: و علیک بالاقبال علی صلاتک، و لا تکفر ،فانما یصنع ذلک المجوس. 
c) روی الصدوق باسناده عن علی (ع) انه قال: لا یجمع المسلم یدیه فی صلاته و هو قائم بین یدی الله عز و جل یتشبه باهل الکفر، یعنی المجوس 
For further information, see:
Ayatullah Jafar Sobhani, Al-Insaf fi Masaela Dama fihal- Khilaf, vol. 1, pg. 169-193.
 The hadith for this subject will come later in the article.
 Sahl ibn Sa’d’s hadith on this matter that Bukhari has narrated is good proof for this claim: “The people were told that men should put there right hand on their left arm in prayer” (Fathul-Bari fi Sharh Sahihil-Bukhari, vol.2, pg.224) because if the prophet (pbuh) had ordered the people to do so, the hadith would have said that the prophet (pbuh) had ordered them, not that “the people were told…”.
 The Hanafiyyah, Shafi’iyyah and Hanabilah all consider closing the hands mustahabb, while the Malikiyyah consider it wajib (Al-Fiqh alal Madhahibil-Khamsah, pg.110).
 Sunan Beyhaqi, vol.2, pp. 72, 73, 101, 102; Sunan Abi Dawud, vol.1, pg.194.
 Al-Wasa’el, vol.4, first chapter of the chapters on the actions of prayer, hadith 1.
 Al-Wasa’el, vol.4, chapter 15 of the chapters on the things that break the prayer, hadith 1.
 Al-Wasa’el, vol.4, chapter 15 of the chapters on the things that break the prayer, hadiths: 2, 3, and 7.
 Jafar Subhani, Fiqhul-Shia al-Imamiyyah wa Mawadhi’il-Khilaf Beynahu wa Beynal-Madhahibil-Arba’, pg.183.