From many different ethnic groups who live in Ethiopia why only two(Amhara people and Tigrayans) consider themselves as Abysinians?
Amara and Tigrean aren’t the only one who consider themselves as Habesha (Abyssinia is the European version of Habesha. There are also others like Agew, Gurage, Argobba, Harari, some Oromo, some Sidama, etc who consider themselves the same. There is no historical evidence that the name Habesha was used to refer only Amara and Tigrean or EthioSemitic in general. Also the meaning of Habesha being mixed is incorrect (at least from majority Ethiopians perspective). Some scholars starting from Hibo Ludolf in the 17th century wrote Habesha and Agazian tribes came from south Arabia to Ethiopia and became the ancestors of the EthioSemitic groups. But there is no concrete proof that Habesha were a given tribe and the Semitic languages of Ethiopia came from south Arabia or outside in general. The inscriptions found in south Arabia which mention Habesha referred to Ethiopians in general who settled there. Being an Ethiopian and a Habesha is almost the same. In Ethiopia, we use Habesha to refer many local things (Habesha chicken, Habesha cabbage, Habesha proudness, Habesha medicine, etc). Many Ethiopians and Eritreans regardless of their ethnicities referred one another as Habesha.
Source: የሀበሻ ምንነትና ማንነት