Even if those offended are just ignorant about the word "Hinayana", why use it?

Uilium, I would ask you, what is your aim, or goal? If liberation is what you are intent upon, the Buddha had this to say in regards to how one should conduct their speech :

Cunda Kammaraputta Sutta:

Skillful Verbal Action

"And how is one made pure in four ways by verbal action? There is the case where a certain person, abandoning false speech, abstains from false speech. When he has been called to a town meeting, a group meeting, a gathering of his relatives, his guild, or of the royalty, if he is asked as a witness, 'Come & tell, good man, what you know': If he doesn't know, he says, 'I don't know.' If he does know, he says, 'I know.' If he hasn't seen, he says, 'I haven't seen.' If he has seen, he says, 'I have seen.' Thus he doesn't consciously tell a lie for his own sake, for the sake of another, or for the sake of any reward. Abandoning false speech, he abstains from false speech. He speaks the truth, holds to the truth, is firm, reliable, no deceiver of the world. Abandoning divisive speech he abstains from divisive speech. What he has heard here he does not tell there to break those people apart from these people here. What he has heard there he does not tell here to break these people apart from those people there. Thus reconciling those who have broken apart or cementing those who are united, he loves concord, delights in concord, enjoys concord, speaks things that create concord. Abandoning abusive speech, he abstains from abusive speech. He speaks words that are soothing to the ear, that are affectionate, that go to the heart, that are polite, appealing & pleasing to people at large. Abandoning idle chatter, he abstains from idle chatter. He speaks in season, speaks what is factual, what is in accordance with the goal, the Dhamma, & the Vinaya. He speaks words worth treasuring, seasonable, reasonable, circumscribed, connected with the goal. This is how one is made pure in four ways by verbal action.

Suzuki Roshi's calls his teaching Hinayana

Suzuki Roshi was in the lineage stream of Zen master Dogen (1200–1253) and was committed to introducing Dogen’s way of practice to the West. Although he recommended studying the many written works of Dogen (few of which were translated into English at that time), it was the spirit of Dogen that was most vital for him. Like Dogen, he did not consider Zen a teaching or practice separate from buddha dharma, or that the Soto school of Zen was either superior or inferior to any other school. He characterized our way as Hinayana (Narrow Vehicle) practice with a Mahayana (Wide Vehicle) mind. Sounds like Suzuki Roshi has a good reason for using the term. Does anyone know what is meant by 'narrow' and 'wide'?

People keep bringing up stuff like Hina used to mean something bad but this was thousands of years ago. Hina now just means small, the standard interpretation is that Hinayana schools only liberate themselves while Mahayana Bodhisattva's continuously liberate themselves as well as other sentient beings therefore it is compared to a Vehicle which is larger as it carries oneself and others as opposed to the Hinayana which only carries oneself.

Why use a word thought by some to be offensive even if the meaning isn't meant to be offensive?

I suppose the reason why, the circumstances in which it's used, varies.

In this answer, Andrei wrote,

... the term "Hinayana" is widely used by Tibetan Buddhism teachers to refer to basic/elementary/foundational (and because of this often simplified) aspects of Buddha-Dharma ... Imagine two teachers discussing their students with each other:

"I have 3 Hinayana-level students, 2 Mahayana-level, and 1 Mahamudra"

In this (hypothetical) example it's "two teachers" using a technical term in private.

So there's no chance of the word being overheard and thought of as offensive.

In the same answer, Andrei used the word "Hinayana". I presume that was because he was answering the question, which was Is there a better term than Hinayana?

The word has been discussed a lot (perhaps too much?) on this site. And obviously, you and I too are both again "using the word" in this topic.

It's used in this question Who follows which yana (Vajrayana, Hinayana or Mahayana)?

I couldn't tell whether the OP wanted to ask about Hinayana or whether he meant to ask about Theravada.

The two words have different meaning so you shouldn't use the one instead of the other (shouldn't say Theravada when you mean Hinayana, and shouldn't say Hinayana if you mean Theravada).

Dhammadhatu's answer answered the question as face value (not as an offensive term but as a yana taught by a Tibetan teacher).

My answer assumed that the OP might have misused the term when asking the question. I made that assumption for two reasons: the OP asked for a "geographical distribution" which is answerable using a map if-and-only-if you assume that the question is asking about Theravada not Hinayana. Another reason why I assumed that meaning is because when I was at school my (non-Buddhist) school-teacher (more or less wrongly) explained that,

"There are two forms of Buddhism: the older Hinayana and the newer Mahayana."

IIRC he might have brought up the same Menshevik/Bolshevik analogy as in Gottfried's answer ... and/or he might have referred to the size of a boat, i.e. a "small boat" is big enough to carry one person whereas a "big boat" is meant to be able to carry many people. I think that my school-teacher's explanation could be obsolete, may be seen as offensive, and may be a very elementary view ... and may be common (e.g. I heard it, so it's "not unheard of") so maybe the OP made a similar use of it.

Those of the ‘Mahayana’ viewed the Theravada School of Buddhism as ‘Hinayana’ - as incomplete realization. For them it was a “lesser” vehicle - word expressing contempt or disapproval. Then the World Fellowship of Buddhists decided unanimously in Colombo in 1950 that the term Hinayana should be eliminated when referring to the Theravada School of Buddhism. The term Hinayana is now a thing of the past.

It was only in the centuries around the birth of Christ that a new school was born, and its adherents called it Mahayana. The adherents of the older schools criticized the Mahayanists, especially for creating new sutras, forging the word of the Buddha. The Mahayanists on the other side reacted to that critique by accusing their opponents of not understanding the teaching of the Buddha at all and for being narrow minded egoists. These views were debated and the Mahayana side of the debate came up with the word “hiinayaana - that any fool could grasp” as an insult, and it stuck. So it does not simply mean "Lesser vehicle". The opposite of mahaa is cuu.la, so this is the normal word for "small".

The term "hiina" is used in the canonical Pali texts in the first recorded sermon of the Buddha, the Dhammacakkappavattanasutta spoken to the five ascetics who became the first five bhikkhus. There the Buddha says:

"These two extremes, monks, are not to be practiced by one who has gone forth from the world. What are the two? That conjoined with the passions and luxury, low (hiina), coarse, vulgar, ignoble and harmful ..."

So one can regard "coarse, vulgar, ignoble and harmful" as definitions of "hiina". Here the Buddha clearly denotes the path not to be practised, as hiina, which without any reasonable doubt means "of low quality". Then Hinayana is not Theravada Buddhism. It is both insulting and historically wrong. Therefore, there is no Hinayana. Wise Buddhists ought to lay that word at rest.

Actually, "hinayana" was originally intended to be offensive, and is also misleading, because it implies a h*m*geneity of the early schools that did not exist. Of course, Mahayanists are not the only ones who developed offensive language concerning the early schools. The Theravadins (who are not one of the original eighteen schools by the way, contrary to popular misconception; see below) referred to the early schools as so many thorns on the tree of dharma. However, the word is also useful because there are not a lot of alternatives, and it has the advantage of being recognizable. The title of my book, Fundamental View, intentionally alludes to the literal meaning of "hina," i.e., base, = basic, using a bit of etymological sleight of hand. I wanted to take what was good about the word and use it, without the pejorative connotation. In my subsequent book, Conversations with the Buddha, I consistently replaced the word with the phrase "the Eighteen Schools," the Hinayana traditionally being identified with the original eighteen schools of early Buddhism. A synonymn for Hinayana is Sravakayana, "the hearers' vehicle," but this is also pejorative. Some people use Theravada as a synonymn for Hinayana, but this is inappropriate since it implies that the relatively late "early" school of Theravada (4th cent. CE) is primary, whereas in fact the Theravadin self-identification with the Sthaviriya (4th cent. BCE) is retrospective and is not mentioned by Warder, for example; this is therefore an ahistorical, sectarian, ideologically motivated back formation, like the word "hinayana" itself, rather like the Jehovah's Witnesses referring to their sect as "original Christianity." Moreover, the Sthavira were not the original Buddhist school, they split from the Mahasamghika, so that one must therefore logically regard the Mahasamghika, precursor of the Mahayana, as the original Buddhist school. Original or presectarian Buddhism is also inappropriate, because the Hinayana consisted of multiple schools and was not presectarian. Incidentally, here is a chronological list of the 18 original Buddhist schools according to A.K. Warder as of circa 50 BCE: Sthaviravada, Mahasamgha, Vatsiputriya, Ekavyavaharika, Gokulika (a.k.a. Kukkutika, etc.), Sarvastivada, Lokottaravada, Dharmottariya, Bhadrayaniya, Sammitiya, Sannagarika, Bahusrutiya, Prajnaptivada, Mahisasaka, Haimavata (a.k.a. Kasyapiya), Dharmaguptaka, Caitika, and the Apara and Uttara (Purva) Saila (quoted from my contribution to the Wikipedia article s.v. Early Buddhist Schools; see also his Indian Buddhism, chap. 9). It is also worth mentioning that the Mahayana does not reject the Hinayana, only one school of which still exists. It is a bodhisattva downfall to disparage the Hinayana. IMHO, the proper Mahayana perspective on the Hinayana is that it constitutes the foundation of Buddhism, much as the foundation of a house; it is not identical with the whole construction of the house, but the whole construction of the house rests on and is supported by the foundation. The house and the foundation need each other. Take away either one, and the whole structure would collapse or be uninhabitable respectively.

In my very first encounters with Buddhism I've always thought, that this is simply the distinguition between "maha" and "hina" in a sense of a larger fraction and a smaller fraction of the sangha in the first larger schism after the second(?) council. An example already known to me was the pair of nouns "Men-shewiki" (smaller fraction) and "Bol-shewiki" (larger fraction) of the communist movement at the early time of Lenin, when the two fractions separated due to different view of things and of how to proceed.
So also the basic term "maha-sanghika" came to me, as "the larger fraction" of the sangha, and I thought, "maha-yana" and "hina-yana" was simply derived from that (physical) comparision of size (the "vehicle of the larger/ smaller fraction").
But with irritating frequency I heard of disgust of buddhists connected with the term "hinayana" - and I'd seen one time in an online discussion someone telling, that "hina" does not simply mean "small(er)" but has a derogatory, diffamating tone.
It seems difficult to find an entry in an actual dictionary (online, don't have a Pali/Sanskrit dictionary at my own), but I found this in a yoga-wiki:

http://wiki.yoga-vidya.de/Hina

Hina (Sanskrit: hina adj. u. n.) ist das PPP der Sanskrit Verbalwurzel (Dhatu) ha und bedeutet: verlassen, zurückgelassen; mangelhaft, fehlend, klein, gering, schwach; kleiner, weniger wertvoll; Mangel, das Fehlen.
(I try to translate but may miss the tone of valuation: "... lost, left behind; buggy, missing, small, low, weak; smaller, less valuable; the lack, the missing")

... while I still do not know the opposite term of "maha" simply with the meaning "small" without a social/valuating tone.

(In principle) I still cannot understand how such a connoted term as "hina-yana" could have at all been born in the sangha of the followers of the Buddha - possibly coined by members simply of "the larger fraction" ("maha-sanghika") even when they thought themselves (and maybe correctly) as practioners of a "wider concept" ...

The disgust of Theravadins seems to me understandable, if I imagine of calling one path/"vehicle" the "omnibus" (mahayana) and the other one the "Bobby car" ("hinayana") using english language - and even to insist on such an implicite valuation in face of the concern with this, which was expressed openly many times and also long times.

A funny/joking example of the tricky relation of ours to the terms "large" and "small" stems from the former socialistic german republic, when the ideal(!) of smallness (in the realms of electronical devices) could not be met as perfect as in "the west", and the people ironically trumpeted: "we have the largest microprocessors of the world!".

So in focusing more on the answering of your question - surely it should be advised to look at common examples, where the "smaller" is the "finer":

• being more focused
• having more concentration,
• being free of a bunch of litter (and -for instance- of fetters)

and -just for the mental exercise of emanicpation from the connotations of "greater" and "less" - one can try to find then actual terms for the advantages-of-the-smaller to get rid of any feeling of being-pissed, of confrontation or even of revenge or of any unkind emotion which might come up when feeling bullied by the term "hina-yana"....

If the mind is 'offended', it is not actually practising the 'Hinayana' (Pali) path. Therefore, the question is non-sequitur.

How many Hinayana practitioners have reached the goal of Arahantship or even Stream-Entry (which is also noble & free)? Many enough.

How many Mahayana practitioners have reached the goal of saving all sentient beings? Zero.

Are we offended when fundamentalist Christians declare Buddhism is evil & Jesus is the only way?

Therefore, what is there to be offended about when the Lord Buddha remained silent & calm about this matter?

Master Gotama, when having directly known it, you teach the Dhamma to your disciples for the purification of beings, for the overcoming of sorrow & lamentation, for the disappearance of pain & distress, for the attainment of the right method & for the realization of Nibbana, will all the world be led [to release], or a half of it, or a third?"

When this was said, the Blessed One was silent.

Uttiya Sutta