Imho it would be much better to watch one's own reaction closely when it comes to the term "hinayana" instead of trying to disabuse others what "hinayana" really means or what one suppose to mean "hinayana".
Of course; however, if there is a teachable moment maybe one can teach.
When I first started reading Buddhist books and started considering myself a Buddhist, one of the books that was most influential was Philip Kaleau's THREE PILLARS OF ZEN. It put Buddhism in terms of actual practice and actual realization. Looking in this book's index: "Theravada, see hinayana" And Theravada/hinayana was characterized by the usual stuff of being monkish, conservative, looking out for oen's own liberation in contrast to the great, liberal open compassionate Mahayana. Who wants to be Theravada/hinayana?
The problem with this is, of course, that it cuts one off from a viable, deep expression of the Dhamma, also setting up an un-versus-them mindset, even if it is subtle. I am NOT advocating going out there and whacking everyone over the head who, for whatever reason, might use the word hinayana in reference to the Theravada, and I agree that we need to be aware of our own reactions to the word, but if there is a teachable moment around the term hinayana and its baggage, it might be useful.
When I got into long drawn debates on e-sandbox over the word and its inappropriaeness when applied to the Theravada, it was not to change the minds of the true believers, though I would hope for an increase in sensitivity to the problems entailed by such sectarian terminology. It was, rather, for others who were reading along, and judging from the fair number PMs I got in response to such efforts, I would say that it was worth the effort, in that people who were likely to look at the Theravada through Mahayana eyes only saw that when looking at the Theravada from a Theravada point of view that there was something there that was far richer, far deeper than the polemical picture of it presented by the sectarian characterization of all things hinayana.