His father was a college physical education teacher and played a significant role in fostering and developing his son's athletic abilities.

His competitors during that period included Romas Ubartas, Vaclovas Kidykas in discus throw, and Saulius Kleiza in shot put.

[8] The agreement enabled Israel to add three athletes — Igor Avrunin in the shot-put and discus, Vadim Bavikin in the javelin and Vladimir Ostrovskiy in the 20-kilometer walk — to its team of Rogel Nachum (men's triple jump) and Orit Kolodni (women's 200 and 400 meters).

He dedicated his time to teaching mathematics and physics, worked in a metal processing factory for four years, and independently explored his passion for computers.

[3] In his free time, Avrunin shared his expertise by mentoring young discus throwers and shot put athletes.

[2] Avrunin's family includes his son, Artur, a basketball player, and his daughter, Angelina, who followed in her father's footsteps to become an accomplished discus thrower.