  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, \cite{Seligman:2020vb} proposed
that the object was made out of molecular hydrogen (H$_{2}$) ice. The question
is whether H$_2$ objects could survive their travel from the birth sites to the
solar system. Here we study destruction processes of icy H$_2$ 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 H$_2$ objects of `Oumuamua-size
before their escape into the ISM. Most importantly, the formation of icy grains
rich in H$_2$ is unlikely to occur in dense environments because collisional
heating raises the temperature of the icy grains, so that thermal sublimation
rapidly destroys the H$_2$ mantle before grain growth.
