Thanks for this open mind question and this shows you do not have dogma about your sect and are seeking the true sect of 73 sect of Islam prophet predicted.
The reason is that according to shia only God can select the Caliph and God selected his Caliph after prophet and he was Ali S.A. and Ali S.A. received divine knowledge of prophet to guide humans and prophet declared it in front of 120,000 Muslims at Ghadir at final Hajj of prophet and Abubakr and Umar and Uthman given Bayat (pledge of alliance) to Ali S.A. but when prophet died and Ali S.A. was at funeral of prophet they left the funeral and made a meeting at Saqifah Bani Saedeh and selected Abubakr as Caliph without any permission from God and prophet and cause misguide of all humanity.
So shia consider the Caliphate the right of Ali S.A. given by Allah and consider this act of Abubakr stealing the position of Caliphate and so consider them hypocrites and all their past good deeds were canceled because of this great sin of disobeying Allah and messenger.
Also another reason is that shia believes that the daughter of prophet, Fatima Zahra S.A. (and her baby in her womb) was martyred at age 18 because of injury made by attack of Umar to home of Ali S.A. to enforce Ali S.A. give Bayat to Abubakr.
This is all the reason.
Shia Muslims for proving their claim about method of selecting Caliph Caliph use some verses of Quran and Ghadir sermon of prophet:
Quran 6:57 says:
إِنِ الْحُكْمُ إِلَّا لِلَّهِ "The command rests with none but Allah:"
(the word حکم in this verse (command) has same root and meaning of
word حکومت meaning government) [6:57]
So if prophet is really messenger of God so according to above verse did appoint the Caliph or not?
or left it for people select it?
Quran 2:30 says:
وَإِذْ قَالَ رَبُّكَ لِلْمَلَائِكَةِ إِنِّي جَاعِلٌ فِي الْأَرْضِ خَلِيفَةً ۖ قَالُوا أَتَجْعَلُ فِيهَا مَن يُفْسِدُ فِيهَا وَيَسْفِكُ الدِّمَاءَ وَنَحْنُ نُسَبِّحُ بِحَمْدِكَ وَنُقَدِّسُ لَكَ ۖ قَالَ إِنِّي أَعْلَمُ مَا لَا تَعْلَمُونَ
And [mention, O Muhammad], when your Lord said to the angels, "Indeed, I will make upon the earth a Caliph." They said, "Will You place upon it one who causes corruption therein and sheds blood, while we declare Your praise and sanctify You?" Allah said, "Indeed, I know that which you do not know." [2:30]
To prove this verse is not generally about placing human in earth this is another verse saying God appointed Ibrahim S.A. as Imam (which is higher rank than Caliph and includes Caliphate position) :
وَإِذِ ابْتَلَىٰ إِبْرَاهِيمَ رَبُّهُ بِكَلِمَاتٍ فَأَتَمَّهُنَّ ۖ
قَالَ إِنِّي جَاعِلُكَ لِلنَّاسِ إِمَامًا ۖ قَالَ وَمِن ذُرِّيَّتِي ۖ
قَالَ لَا يَنَالُ عَهْدِي الظَّالِمِينَ
And [mention, O Muhammad], when Abraham
was tried by his Lord with commands and he fulfilled them. [Allah]
said, "Indeed, I will make you a leader for the people." [Abraham]
said, "And of my descendants?" [Allah] said, "My covenant does not
include the wrongdoers." [2:124]
This verse uses exactly the Arabic word for Caliph.
If God appoints Caliph so did God appoint the Caliph after prophet? or left it for people select it by voting or shura (meeting) or etc. anyway voting shura,.. are not appointing by God and are appointing by people.
Also this verse:
يَا دَاوُودُ إِنَّا جَعَلْنَاكَ خَلِيفَةً فِي الْأَرْضِ فَاحْكُم
بَيْنَ النَّاسِ بِالْحَقِّ وَلَا تَتَّبِعِ الْهَوَىٰ فَيُضِلَّكَ عَن
سَبِيلِ اللَّهِ إِنَّ الَّذِينَ يَضِلُّونَ عَن سَبِيلِ اللَّهِ لَهُمْ
عَذَابٌ شَدِيدٌ بِمَا نَسُوا يَوْمَ الْحِسَابِ
[We said], "O David, indeed We have made you a successor upon the
earth [Caliph], so judge between the people in truth and do not follow
[your own] desire, as it will lead you astray from the way of Allah."
Indeed, those who go astray from the way of Allah will have a severe
punishment for having forgotten the Day of Account. [38:26]
uses exactly the Arabic word for Caliph. and God says:
We made you Caliph. so did God do the same for Caliph after prophet? or this time God changed his mind and left it people make Caliph by voting or shura or etc?
If Imams could not be political Caliph it was because Umayyids and Abbasids did not let them and kept them in home arrest or killed them and warned them to not have any political activity.
what you think? Imam Husain (sa) go to Yazid and say: please give me the politial power. and Yazid say OK come sit here in my chair and I go home good bye?!!
You are so simple thinking.
Who Killed Imams of Shia? they all were killed by fake Caliphs because they wanted to be political leaders.
Shura is for when God did no specify some thing or any part of religion?
for example can some Muslims make shura and change Zuhr Salat to 2 rakah? or remove fasting from Islam by shura?
(every single part of this answer can be proved from Quran and sunni ahdith books. but because you asked for short answer I skipped them,. but you can ask each part in separate question)
Hadith of the pond of Khumm
Fatima ['a] The Gracious