What does 'fungus-growing' mean?
An entomologist is an insect expert. The sentence seems to refer to a species of termite that cultivates a fungus within its mounds to provide food for the colony. That is, they 'grow fungi' - nothing to do with growing up.
We sometimes speak of a district that specialises in a particular crop as a wheat-growing area, or a vine-growing district. We wouldn't use it of grass (too universal) or of meat (you raise animals, not grow them).