Why is there not a gender-neutral singular pronoun in English?

There is: "they".

It's a centuries-old usage in English, but for whatever reason - 19th century peeves most likely - traditional grammar considered it wrong for a long time (maybe on grounds that "they" is also plural - though no-one objected to "you" being singular or plural). However, "singular they" has been revived since the late 20th century, in the light of the need for a gender-neutral pronoun as a non--sexist usage, and a number of major grammatical authorities have endorsed it.

Check out:

* Merriam-Webster OK's Singular-They http://www.bilerico.com/2011/10/merriam-webster_ok...

* Oxford Dictionaries / ‘He or she’ versus ‘they’ http://oxforddictionaries.com/words/he-or-she-vers...

* Pullum & Huddleston / A Student's Introduction to English Grammar / semantically singular they http://books.google.co.uk/books?id=qlxDqB4ldx4C&pg...

* Singular “they” and the many reasons why it’s correct http://motivatedgrammar.wordpress.com/2009/09/10/s...

> my former teacher emphasized that the word "they" was plural

It's very difficult to mentally over-ride stuff that we've been taught. But one of the stepping stones to acquiring a mastery of English is to know when to. In many situations of grammar, teachers parrot bogus rules that go against real usage - including educated usage - and this is one of them. Merriam-Webster, page 901 onward, has extensive evidence of its use over six centuries by writers whose credentials are impeccable: http://books.google.co.uk/books?id=2yJusP0vrdgC&pg...

No, it can be not suitable in formal settings. Sure, "their" is gender-neutral, nevertheless it's still plural! There's a difference between linguistic evolution and breaking the principles -- the website online you're quoting doesn't look to realize the change. You cannot press a plural into service simply since there's no singular identical. "His or her" is quality, if cumbersome. I simply try to rewrite sentences to preclude the main issue whenever i will be able to -- casting it within the plural to begin with is the simplest fix.

On the internet, I've seen some people use 'xe' for a gender neutral pronoun. I don't think this is something that will transfer to real life, however.

I know many native speakers that just use 'they' instead of he or she.

English is a weird language. The only real rule is that there are countless exceptions.

Most European languages make the same distinction. Il est, elle est. Er ist, Ihr ist. You can say one, as in one says, on dit.

One could always use "one". http://en.wikipedia.org/wiki/One_(pronoun)