If Prophet Abraham was infallible, why did he lie then?

According to the Quran, prophet Abraham(a.s) broke all the Idols which were worshiped at his time into pieces except the chief of them¹ and when the people (who had left the city for some ceremonies) returned to the city and realized that somebody had broken the Idols they asked prophet Abraham(a.s) whether he had broken them or not.²
then prophet Abraham(a.s) answered:

Rather, this - the largest of them - did it, so ask them, if they should [be able to] speak."³

Prophet Abraham(a.s) said something that was not according to the reality and since Abraham was a prophet and an immaculate person that would never tell a lie, there have been stated different matters upon this Qur'anic sentence.

What seems the best of all is that Abraham(a.s) decisively attributed this action to the great idol, but all references testified to the fact that he did not intend to say it earnestly. He wanted to make the baseless superstitious notions of the idol worshippers' manifest to them. Even the people at that time didn't believe that the idols were broken by the largest one, because it was clear to everyone that the idols couldn't move, and even they realized that prophet Abraham(a.s) wanted to teach them a lesson and he didn't mean what he said.

What seems the best of all is that Abraham(a.s) decisively attributed this action to the great idol, but all references testified to the fact that he did not intend to say it earnestly. He wanted to make the baseless superstitious notions of the idol worshippers' manifest to them. Even the people at that time didn't believe that the idols were broken by the largest one, because it was clear to everyone that the idols couldn't move, and even they realized that prophet Abraham(a.s) wanted to teach them a lesson and he didn't mean what he said.

In our daily sayings there are many instances similar to this meaning when, in order to nullify the speech of the opposite party and to condemn him, we put his indisputable affairs in front of him in the form of an imperative, declarative, or interrogative sentence, and this is not a lie at all. A lie is something that has not a frame of reference with it.

This great method that was used by prophet Abraham not only didn't have negative consequences but it had a great and positive influence on Idol worshippers, because it made them ponder on the fact that these soulless pieces of stone could not even move or speak, let alone help their worshipers,

This great method that was used by prophet Abraham not only didn't have negative consequences but it had a great and positive influence on Idol worshippers, because it made them ponder on the fact that these soulless pieces of stone could not even move or speak, let alone help their worshipers, as it is mentioned that after the claim of prophet Abraham they said:

So they returned to [blaming] themselves and said [to each other], "Indeed, you are the wrongdoers."³

This was an intelligent method used by the prophet to make them admit against their own beliefs and say:

"You have already known that these do not speak!"⁵

At this moment prophet Abraham(a.s) used this confession against them and said:

Then do you worship instead of Allah that which does not benefit you at all or harm you? Uff to you and to what you worship instead of Allah. Then will you not use reason?"⁶

And this is how prophet Abraham(a.s) defeated the worshipers of idols with wisdom and good instruction and argued with them that is best.

There has been cited a tradition in the book of Kafi narrated from Imam Sadiq (as) who said:

“He (Abraham) said: ‘Nay, it was done by this, the chief of them’ for he intended to improve their thoughts and to tell them the idols could not do such an action.”⁷

[1] فَجَعَلَهُمْ جُذَاذًا إِلَّا كَبِيرً‌ا لَّهُمْ لَعَلَّهُمْ إِلَيْهِ يَرْ‌جِعُونَ
[21:58]
[2] قَالُوا أَأَنتَ فَعَلْتَ هَـٰذَا بِآلِهَتِنَا يَا إِبْرَ‌اهِيمُ
[21:59]
[3] قَالَ بَلْ فَعَلَهُ كَبِيرُ‌هُمْ هَـٰذَا فَاسْأَلُوهُمْ إِن كَانُوا يَنطِقُونَ
[21:63]
[4] فَرَ‌جَعُوا إِلَىٰ أَنفُسِهِمْ فَقَالُوا إِنَّكُمْ أَنتُمُ الظَّالِمُونَ
[21:64]
[5] ثُمَّ نُكِسُوا عَلَىٰ رُ‌ءُوسِهِمْ لَقَدْ عَلِمْتَ مَا هَـٰؤُلَاءِ يَنطِقُونَ
[21:65]
[6] قَالَ أَفَتَعْبُدُونَ مِن دُونِ اللَّـهِ مَا لَا يَنفَعُكُمْ شَيْئًا وَلَا يَضُرُّ‌كُمْ . أُفٍّ لَّكُمْ وَلِمَا تَعْبُدُونَ مِن دُونِ اللَّـهِ ۖ أَفَلَا تَعْقِلُونَ
[21:66,67]
[7] Nur-uth-Thaqalayn and Burhan, following of the verse