Why do the Shiites believe in the infallibility of their Imams?

In order to prove the infallibility of the Imams, Shiite theologians have put forth various rational and religious proofs. One of their rational arguments is that Imam is the guardian of shri'ah, therefore he should be infallible.
The prime responsibility of Imam is guarding the religion and keeping it safe from any alteration and that's why he should be immune from making mistakes, unless one posits that for keeping the religion safe and meeting the upcoming needs of human there is no need for an infallible Imam and there are other factors that can lead to that. We should see whether the religion can remain safe from alteration without an Imam or not? The ways imaginable through which the religion may remain intact and applied correctly when facing new issues are the Quran, traditions of the Prophet (PBUH), consensus, analogy and the principle of non-existence of a rule unless proved otherwise and a combination of all of them.

Imam is the guardian of shri'ah, therefore he should be infallible

We will examine each of them respectively:

The Quran:

The Muslims unanimously agree that the Quran on its own cannot keep the religion safe because it is prone to various interpretations. On the other hand, events that occur along the history are of different types and not everyone can refer to the Quran to deduce the ruling pertaining to a specific case.

The tradition:

The prophetic tradition also cannot keep the religion unaltered during the history because of the above-mentioned reason.

The prime responsibility of Imam is guarding the religion and keeping it safe from any alteration and that's why he should be immune from making mistakes

Consensus:

The validity of consensus depends on its indication of the existence of an infallible Imam among those who agree on an issue. If the Imam is not present among them then their consensus loses its validity because when the mistake of every person in a group is probable, then the mistake of the whole group is also probable.

Analogy:

Analogy means to refer to other similar cases in order to infer the ruling for a particular case. Because analogy only leads to a weak guess it is not an approved source in deducing religious rulings. Thus it cannot keep the religion safe.

The Muslims unanimously agree that the Quran on its own cannot keep the religion safe because it is prone to various interpretations. On the other hand, events that occur along the history are of different types and not everyone can refer to the Quran to deduce the ruling pertaining to a specific case

The principle of non-existence:

It means that whenever we don't find a ruling from God regarding a specific case we can deduce that the ruling for that case is neither obligation nor illegality. This principle also cannot safeguard the religion because were it sufficient then appointing the prophets and commissioning them with guiding people would not be necessary. Appointing prophets and sending books with them to guide people shows that there are divine rules which man's intellect cannot always infer, that is, there is a need for a reliable person who can deliver God's rules to people.

A combination of all of them:

A combination of all of them does not also rid us from the need to a guardian for the religion because on the one hand there are fabricated traditions that contradict the Quran and on the other hand analogy is not an acceptable source of knowledge and the faculty of reason is not sufficient. Thus all of them put together will not also keep the religion safe.
Therefore, there must exist an infallible Imam who can keep the religion safe from any alteration and change.