The Noble Scholar, Shaykh Saalih al-Fawzaan (Member of the Permanent Committee of Major Scholars, Kingdom of Saudi Arabia) mentioned in the highly beneficial booklet 'A Glimpse at the Deviated Sects' (Salafi Publications), concerning the roots of the Ashaa'irah:

The madhhab of the Ashaa'irah branched off from the Mu'tazilah and the name is an ascription to Abul-Hasan al-Asha'aree (may Allaah have mercy upon him) who used to be a Mu'tazilee, then Allaah favoured him and he recognised the falsehood of the Mu'tazilee madhhab. So he stood in the mosque on a Friday and announced his disassociation from the madhhab of the Mu'tazilah. Then he took off his thawb (long shirt) and said: "I have discarded the madhhab of the Mu'tazilah just as I have discarded this thawb of mine".
 
However, he then followed the madhhab of the Kullaabiyyah, the followers of 'Abdullah bin Sa'eed bin Kullab'', Who used to affirm seven attributes and negate all the others (Ibn Kullaab) said:

"This is because the intellect only points towards or indicates seven attributes: Knowledge, Power, Will, Life, Hearing, Sight and Speech". And he said: "This is what the intellect indicate:, as for that which that the intellect does not indicate, then it is not affirmed."

Then, Allaah blessed Abul-Hasan al-Ash'aree, so he left the madhhab of the Kullaabiyyah and returned to the madhhab of Imaam Ahmad bin Hanbal, died 241H, (may Allaah have mercy upon him) and he said: "I say that which the Imaam of the Ahlus-Sunnah wal-Jamaa'ah, Ahmad bin Hanbal says' "Allaah made istiwaa (ascension) over the Throne and He has a Hand and a Face." And in his books: 'Al-Ibaanah 'an Usoolid-Diyaanah' and 'Maqaalaat al-Islaamiyeen wa Ikhtilaaf al-Musaleen', and he mentioned that he was upon the madhhab of Imaam Ahmad bin Hanbal. However he held on to some ideas which differed from the truth.

However most of his followers remained upon his previous madhhab, the Kullaabiyyah, and thus they are called al-Ashaa'irah, an ascription to al-Ash'aree during his first madhhab.
 
However since he returned to the madhhab of Ahlus-Sunnah wal- Jamaa'ah, then to ascribe this Asha'ree madhhab to him is injustice. It is more appropriate to say 'the madhhab of the Kullaabiyyah' and not the madhhab of Abul Hasan al Ash'aree. This is because he repented from it as mentioned in his book 'Al-Ibaanah 'an-Usoolid-Diyaan’ where he clarified his return and his clinging to what Ahlus-Sunnah wal-Jamaa'ah were upon, especially Ahmad bin Hanbal, even if he (Abul Hasan al-Ash'aree) had some remaining deviations, such as his statement regarding the Speech of Allaah: "Verily it is the meaning itself which stands alone and the Quraan is an interpretation of the Speech of and not His Speech itself"

This is the madhhab of the Ashaa'irah which split off from the Mu'tazilah and the Mu'tazilah split off from the Jahmiyyah, and then many more sects branched off, all having their foundation in the madhhab of the Jahmiyyah.