Regarding Imam Abu Hanifah’s allegedly having studied under Imam Ja’far as-Sadiq, please be informed as follows:
Imam Abu Hanifah was the pupil and intellectual successor of his mentor, Hammad ibn Abi Sulayman, who was the successor to Ibrahim an-Nakha’i, who was the successor to his uncle ‘Alqamah ibn Qays an-Nakha’i, who was the successor to Sayyiduna ‘Abdullah ibn Mas’ud, who was sent as a teacher to the city Kufah by Amir al-Mu’minin Sayyiduna ‘Umar ibn al-Khattab. This chain of intellectual descent is known to anyone knowledgeable of the legislative history of Islam.
In fact, Imam Abu Hanifah held his dicourses at the very same place in the masjid of Kufah where Ibn Mas’ud used to teach. This teaching circle was passed down generation after generation, by the men whose names you have just read: From Ibn Mas’ud to ‘Alqamah; from ‘Alqamah to Ibrahim; from Ibrahim to Hammad; and ultimately from Hammad to Abu Hanifah, after whom it was occupied by three of his students successively: firstly Zufar ibn Hudhayl; then Abu Yusuf; and then Muhammad ibn al-Hasan.
Now, regarding the link between Abu Hanifah and Ja’far as-Sadiq, you need to keep in mind the following:
Imam Abu Hanifah was born in the year 80 AH
Imam Ja’far as-Sadiq was born in the year 83 AH
In other words, not only were they contemporaries; but Abu Hanifah was 3 years older than Ja’far as-Sadiq.
Imam Abu Hanifah’s education took place in Kufah, in the school originally established by Ibn Mas’ud. Like other ‘ulama of his time, he used to go to Hijaz for Hajj, and passing through Madinah, he used to benefit from the knowledge of eminent men of learning, such as the father of Imam Ja’far as-Sadiq, namely Imam Muhammad al-Baqir. Many of the ahadith he narrates from Imam Muhammad al-Baqir are documented in the books of his pupils Abu Yusuf and Muhammad ibn al-Hasan.
It is true that Imam Abu Hanifah does narrate some ahadith from Imam Ja’far as-Sadiq. But that was according to the habit of the ‘ulama to narrate from even their contemporaries. If that alone is to be taken as evidence that Imam Abu Hanifah “studied” under Imam Ja’far as-Sadiq, then we will be bound to conclude that Imam Ja’far as-Sadiq similarly learnt from people other than his father, such as Ibn Shihab az-Zuhri, ‘Ata ibn Abi Rabah, ‘Urwah ibn Zubaur and Muhammad ibn al-Munkadir. Imam Ja’far as-Sadiq has narrated hadith from all of these men, and even others besides them. (Tahdhib al-Kamal vol. 5 p. 75)
In the year 132 the Abbasids came to power, having ousted the Umayyads. Abu Hanifah was then 52 years of age. The Abbasid khalifah Abu Ja’far al-Mansur wanted Abu Hanifah as his chief justice, which post he refused. In order to escape the vengeance of the khalifah, Abu Hanifah betook himself to the Hijaz where he spent the next 2 years. It is in terms of this sojourn in the Hijaz that he is reported to have said, “Were it not for the 2 years, Nu’man (i.e. Abu Hanifah) would have been destroyed”. Creative Shi’i imaginations would have us believe that what he actually meant thereby was that it was during this period that he gained his knowledge at the feet of Imam Ja’far as-Sadiq. The absurdity of this can be seen from the fact that by that time he was already so famous as a man of learning, that he was sought by the khalifah as the chief justice. Apart from that, he was, as already shown, over 50 years of age.
There is a famous story in circulation about Imam Ja’far as-Sadiq posing certain questions to Imam Abu Hanifah regarding the use of Qiyas (analogy). You should be informed that the story appears in this form in Shi’i books such as al-Kafi. In the Sunni literature it appears with significant changes.
First of all, the discussion is not between Abu Hanifah and Ja’far as-Sadiq, but between Abu Hanifah and Muhammad al-Baqir.
Secondly, the story goes as follows:
Al-Baqir asks Abu Hanifah if he is the one who is changing the Deen of his (al-Baqir’s) grandfather (Rasulullah sallallahu `alayhi wasallam) through the use of Qiyas. Abu Hanifah denies that he is changing the Deen. In order to demonstrate the falsehood of the rumours, he then goes on his knees in front of Imam al-Baqir and uses the comparison between (1) the share of a man and a woman in the spoils of war; (2) fasting and prayer with regard to a woman in menstruation having to pray in the former and not the latter; (3) urine and semen in respect of the method of purification for either one. After this lucid demonstration of his usage of Qiyas only where there is no textual evidence, and strictly adhering to the authority of text where it exists, Imam Muhammad al-Baqir stands up and kisses Imam Abu Hanifah on his forehead. (Manaqib Abi Hanifah by al-Kardari, p. 99)
It was only later that the Shi’ah would adapt the story to suit their own particular needs.