The famous scholar of the tabi’een Al-Hasan al-Basri was teaching a halaqah when the topic came up of a Muslim who commits major sins. Al-Hasan said that such a person, although a sinner, is still undoubtedly a Muslim. The belief of Ahlus Sunnah wal Jama’ah is that the commiting of a sin, no matter how major, does not expel one from Islam (with a slight disagreement over the sin of abandoning prayer). One man sitting in the halaqah by the name of Wasil ibn Ata refused to accept this, saying that a person committing a major sin was neither a believer nor a disbeliever. This concept, of being neither Muslim nor Kafir, is one of the most emblematic positions of the Mu’tazilites and you’ll find it referred to as al-manzilah baynal manzilatayn (a state between two states). He withdrew (‘itizal) from the halaqah and started his own, receiving the label of Mu’tazilite from Al-Hasan al-Basri.
Side note: The Mu’tazilite theological ideology we’re discussing here is completely different from the Mu’tazilite political ideology which existed in the time of Ali (ra) and Muawiyah (ra). In that context, “those who withdrew”, i..e Mu’tazilites, refers to those people who refused to take sides between the two companions. No relation at all to this theological group.
Now, the basis of Mu’tazilism was a melding of Hellenistic thought with Islam. Some people like to tout Muta’zilites as the “rationalists” of Islam. This is just plain stupid. It was not “rationalists” vs “traditionalists.” There were several different schools on the relationship between reason and revelation and the Mu’tazilites were but one attempt. The Falsafa were one important group, putting even more weight on Greek thought (realize that for these groups, reason=Greek thought). The Asha’ira, which rose as a response to the Mu’tazilites were yet another group. The Hanbalis (theological school, not fiqh) were yet another.
Ok, as to why Mu’tazilites are at the very least, ahl-Bid’ah (you can dismiss in totality someone who says otherwise because they clearly have no knowledge of Islamic theology). I’ll talk about two of their most important points but the entire movement can be summarized very succinctly: When a text of either the Qur’an or Hadith contradicted with reason (and again, reason here is Greek thought), the Qur’anic/Hadith text had to be rejected in favor of reason.
So, because of their Hellenistic framework, certain positions were taken that deviated completely from the normative tradition. The term Mu’tazilites was actually given to them by their opponents (cue the flood of progressives saying we should stop using the term then). They called themselves Ahl al-Tawhid wal ‘Adl. The first is monotheism and the second is justice. I’ll talk about their stance on these two:
Monotheism in the Mu’tazilite conception was a complete denial of the attributes of Allah (swt). This had to do with the way they rationalized the existence of Allah. Their proof is detailed and there’s little point in repeating it here, but suffice it to say, that for their argument to work, Allah ﷻ had to be devoid of all attributes. Mercy, Wisdom, Knowledge, Power, etc. All the attributes we read in the Qur’an, at the end of almost every other ayah? They dismissed them or reinterpreted them. Because for them, the need to maintain the internal consistency of their theology outweighed the very clear meaning of the Qur’an.
In their quest to have a “just” religion, they also had deviant beliefs in regards to fate and free will. In this, they echoed the beliefs of the Qadariyyah. In fact, some historians argue that the Mu’tazilites were the Qadariyyah; that they were simply an expansion of that group into broader issues. They believed that humans have total free will and that Allah is ignorant of the future. In fact, there’s a famous narration of a Mu’tazilite scholar on this issue where a hadith on the matter was spoken to him. He replied, “If I heard this narration straight from the sahabi, I would call him a liar. If I heard it from the Prophet, I would tell him he misunderstood Allah. And if I heard it from Allah, I would tell Him that this is not why He created us.” So as you can see, there’s plenty of ground to stand on for those who consider the Mu’tazilites to be beyond ahl bid’ah and to be kuffar.
Now, with all that said, Mu’tazilite beliefs did vary at different stages of Islamic history and even between groups during a certain era. Their condition straddles the line between kufr and bid’ah. Because some of these issues are quite esoteric and it’s possible for an honest person to get caught up and be sincerely convinced of the validity of the arguments, most scholars label them as ahl-bid’ah and not kuffar. Allahu a’lam which one is more accurate, but there’s no denying that they are outside of mainstream Islam.