Unlike French, Spanish, Italian, Portuguese and a host of other languages,
English does not have much in the way of feminine vs. masculine distinctions.
So how is that "obsessed with gender"?
I expect he's actually referring to the fact that English possessives
agree in gender with the possessor instead of the possessed, as would
happen in, say, French. This can make third-person gender-neutral
constructs hard to complete: think about how you should complete the
following sentence: The student did not turn in ____ homework.
In contrast to Romance languages and many others, English in general
distinguishes much less between male and female versions of, say, an
occupation: in French, you'd have to pick between étudiant and
étudiante. Also note that we have a single third-person plural variant
("they", which can also be used as a gender-neutral singular pronoun,
although some would frown at such a usage [1]), in contrast between
French where you are forced to pick between "ils" and "elles."
As for obsessed about number, note that we do not distinguish between
singular and plural second-person and have not for 400-500 years. "They"
does a remarkably good job about conveying uncertainty about number as
well as gender too, and it wouldn't surprise me if it became more
prevalent in singular third-person in 400 years.
Note, however, that this kind of inflectional agreement in English is
largely limited to the various inflections of pronouns; in many Romance
languages, inflection is required on adjectives and the verbs themselves.
[1] Singular they has even been used by Shakespeare, so I would
personally classify attempts to outlaw it on the same level as those who
hate sentences ending in prepositions: it may be bad style, but
incorrect English it is not.