The first interstellar object observed in our solar system, 1I/2017 U1 (‘Oumuamua), exhibited a number of peculiar properties, including extreme elongation and acceleration excess. Recently, Seligman & Laughlin proposed that the object was made out of molecular hydrogen (H2) ice. The question is whether H2 objects could survive their travel from the birth sites to the solar system. Here we study destruction processes of icy H2 objects through their journey from giant molecular clouds (GMCs) to the interstellar medium (ISM) and the solar system, owing to interstellar radiation, gas and dust, and cosmic rays. We find that thermal sublimation due to heating by starlight can destroy ‘Oumuamua-size objects in less than 10 Myr. Thermal sublimation by collisional heating in GMCs could destroy H2 objects of ‘Oumuamua-size before their escape into the ISM. Most importantly, the formation of icy grains rich in H2 is unlikely to occur in dense environments because collisional heating raises the temperature of the icy grains, so that thermal sublimation rapidly destroys the H2 mantle before grain growth.