A colleague recently complained to me of the usage of relatable in student writing. It appears to derive from intransitive relate, OED sense 9, attested only from 1947:
intr. With to. To understand or have empathy for; to identify or feel a connection with. Also without construction.
Most adjectives formed from verbs with suffix -able or -ible are formed from transitive verbs so as to modify what would be their direct objects, as readable modifies what one might read; but this is no invariable rule, since laughable modifies what one might laugh at. So the intransitivity of this sense of relate is not a valid objection.
The Google Books Ngram utility suggests that relatable peaked in the seventies (though it cannot well distinguish usages with a "to s.t." from those without, the latter only being in question here). And indeed these usages of both relate and relatable strike me as redolent of that era's youth culture or counterculture; they seem to function primarily as a kind of slang, i.e., to identify the user as a member of that culture, hipper than those who might use understand and understandable for the same purposes. If that is all that is going on, such usages are generally ill-suited to formal academic writing. But is there more to it than that in this case?