'Hinayana' is a term invented by the Mahayanists in the long history of Buddhism. The 'Three Vehicles' is also the classification used by the Mahayanists to show their superiority over other traditions. Why I brought this up in Theravada Buddhism forum is because when I read the lecture notes by Prof. G.A. Somaratena on Theravada Buddhism (Lesson Unit 1), I was surprised that he agreed to use the term 'Hinayana' to associated it with Theravada and Sarvastivada schools and employed the classification/term of the 'Three Vehicles" to elucidate the three major Buddhist traditions
Overhere I would like to quote the introduction of an article written by Chan Khoon San & Kara A Lie - 'No Hinayana in Buddhism' in order to register my dissenting opinion:
"For centuries, the reputation of the early Conservative Buddhist schools had been stigmatized by the term 'Hinayana', used indiscriminately to label them. The Pali/Sanskrit word "Hinayana" means "low, undesirable, or despicable vehicle." This label is highly derogatory and false. Today the law considers it as defamatory! Buddhists and non-Buddhists alike are strongly advised to stop using it to describe any Buddhist school, whether existing or extinct. There is no legal or moral justification in using this libellous term anymore! There is no Hinayana in Buddhism. (it is advised that you read further this article that can be found in the internet)
Furthermore, in 1950, the World Fellowship of Buddhists inaugurated in Colombo, unanimously decided that the term 'Hinayana' should be dropped when referring to Buddhism existing today in Sri Lanka, Thailand, Burma, Cambodia, Laos, etc.
In view of the above and many other reasons, the use of these two terms is grossly inappropriate least to say appeared in academic teaching papers of a highly esteemed establishment.
No Hinayana or Mahayana
The word to describe superior or inferior vehicle is a contradiction to the teaching of Four Noble Truth. As in the second Noble Truth, one of the root cause of suffering is due to the Delusion (Ignorance) that 'I' or 'Self' exist permanently, or attachment to ego. When any person think that this Buddha's teaching is small or big vehicle, actually it is due to the attachment to 'ego'. Then, how can one liberate from there if still attached to this notion.
Spiritual practitioners with meditation, contemplation and taking precepts or vows will not have this notion of Hinayana. If the Mahayanist has this notion, then one is not Mahayanist either, because one is discriminate or has the thinking of superiority, thus become egoistic.
The word Hinayana was invented by the non spiritual people who misunderstand the path even after taking the Bodhisattva vows. If one look study the history of Indian Buddhism, there was no schools termed as Hinayana. Both Theravada and Sarvastivada are from the Sthavira school. The Mahayana term in Sanskrit was actually derived from Prakrit word Mahajhana.
The Bodhisatva ideal was already part of the early Buddhism. The precursors of Boddhisatva ideals are found in Majjhima Nikaya, Digha Nikaya and Madyama Agama. The oldest Astarika Prajnaparamita fragments were discovered from the sub-school of Mahasamghika, the Caitika school in Amravati written in Prakrit language. Even though it was dated between 47 to 147 CE, but some scholar suggest that this ancient Buddhist sites in the lower Kṛiṣhṇa Valley, including Amravati, Nagajurnakonda and Jaggayyapetta "can be traced to at least the third century BCE, if not earlier” as archeology researched done by scholar Sree Padma.
So, there are no Hinayana or Mahayana, but all are from the lineage of Early Buddhism, either from one of the 18 early schools or combination of few of the early 18 schools.