The correct option is 2 only
Explanation
By the first century CE, Buddhism witnessed a significant schism resulting in the emergence of a new school of thought known as Mahayana (the Great Vehicle). This school introduced the worship of Buddha images and the Bodhisattva ideal, distinguishing itself from the earlier, more orthodox traditions.
Statement 1 is Incorrect:
Supporters of the Mahayana tradition coined the term Hinayana to describe the older, orthodox schools. 'Hinayana' literally translates to the "Lesser Vehicle" or "Inferior Vehicle." This terminology was used to contrast the older tradition's focus on individual salvation (Arhatship) with the Mahayana goal of universal salvation for all beings.
Statement 2 is Correct:
The term 'Hinayana' was pejorative and implied inferiority. Consequently, followers of the older tradition did not accept this label, nor did they wear it with pride. They referred to themselves as Theravada, meaning "The Way of the Elders" or "The School of the Elders," emphasizing their adherence to the original teachings and monastic rules of the Buddha.
Key Takeaway:
'Hinayana' is an exonym used by Mahayanists to denote the older Buddhist sects; the practitioners of the surviving older tradition identify themselves as Theravada.