They actually did explain this. His motivations basically come down to population control.
His own homeworld died off because they ran out of resources. At the time, his proposal to fix it was to kill off half the population, and that way the people remaining would survive and have a good standard of living. They didn't listen (and he got called "Mad" for proposing this) and went extinct.
Same with Gomorra's homeworld. According to him, they lived in famine and poverty until he killed off half of them, and now they enjoy a much better standard of living and no kids there have to go hungry.
So that's basically his motive in the movie. He thinks sentient beings will end up dying or killing each other off due to lack of resources unless he reduces the population. You're not supposed to agree, but he does have a motive.