Is this quote from the book ”English Grammar Simplified” sexist?

I don’t think it’s sexist…I think it’s improper English.

Definitely.
It has no gender using “everyone” then gets it wrong by using “his”, this should be replaced with the word “their”.
Added: Why are there aircraft “Cockpits” now we have female Pilots? Some now refer to this now as the “Flight Deck”.

It does sound kind of sexist, yes. This debate has been going on for a long time. Generally it’s resolved by saying “his or her” or “their” instead of choosing either the masculine or feminine possessive. Where I work, we try to avoid writing sentences that force us to use this kind of phrasing. I might say, “…people who wish to understand English grammar and improve their speech and writing.”

No, it’s just implying that males are the only ones who need to improve their speech and writing. jk.

Seriously, though, he, his, him, whatever, they’re generic terms and people need to get over the fact that it is.

If you’re going to say that it’s sexist then you might as well argue that languages that use gender-specific articles are sexist. Why is chair feminine and car masculine? Obviously, there’s some sexism going on there. *sarcasm*

Why do we use female terms to describe boats and cars? It’s in the language and we can’t change it.

Also, it’s awkward when reading a really long sentence to keep reading he/she or his/her every time a person is indicated.

Unbunch your shreddies Robert. ” Use of generic-isms is not ‘ist’ in any form. Should it be perceived as such,it will be a self-evident admission by those who do the strident perceiving that they have no knowledge of English grammar or composition.

That’s a nonsensical interpretation – it’s simply grammatically correct English.