When you hear someone going on about The Rules in English, you should be on your guard, just as when some personage with a clerical collar starts to say, "The Church has always taught. ..." You are likely to hear, at best, a misconception, at worst, an outright whopper.
I have tried to establish the usefulness of distinguishing rules from conventions, shibboleths, superstitions, house style, and individual aesthetic preferences.
Take, for example, the eighteenth-century convention of separating subject from verb with a comma. Use it today, and your English teacher will mark it as an error.*
Or, better, take the custom of typing two spaces after a period ending a sentence. It was drilled into generations of students in typing class as a Rule, and it became a firmly established habit. Just try to explain to these people that proportional type in word processing software has made that obsolete, and you get reactions like those of gun owners convinced that black helicopters are in the air, full of jackbooted federal thugs determined to loot their arsenals.**
The problem, then, is making careful distinctions between rules and non-rules. It is complicated by dogmatism.
At Precise Edit's Blog, David Bowman (@Precise Edit on Twitter) recently published a post, "The Most Common Grammar Mistake." After explication of agreement of subject, verb, and pronoun, "the most common grammar mistake" turns out to be "to use a singular subject (one person or thing) with a verb in the third person singular (the verb has the 's') but then refer to the subject with a plural pronoun." Mr. Bowman has singular they in his crosshairs.
Mr. Bowman's advice is entirely traditional and orthodox, but I wish that he were less given to flat statements of right and wrong. His readers would be better informed to learn that as published, edited writing has grown more informal, the singular they common in speech has become increasingly acceptable, or that many established, reputable writers, including some notable for their finicky usage, have used singular they over the centuries.
I suppose it will be argued it would be futile to barrage some audiences, such as schoolchildren and adults learning English, with such complexities, and I hardly think that it would be a good idea to deposit the Huddleston-Pullum Cambridge Grammar of the English Language on every elementary pupil's desk (though Mark Liberman suggests at Language Log that a linguistically informed curriculum is not fanciful).
But we don't tell students, at least not the promising ones, to stick with addition, subtraction, and multiplication because trigonometry and calculus are hard to understand. If we want them to achieve more sophisticated and better-informed writing, they will have to be introduced to the complexities.
Creaky schoolroom grammar and dogmatism were probably never equal to the purpose; they are less so now.
*I have wielded the English teacher's red pen, and have come to question the utility. Some poor devil gets a paper that looks as if I have butchered a hog on it, and everything is wrong, everything is an error of equal weight, and all of it is bewildering. With the comma between subject and verb, for example, it would be better not to count it as a error but merely to say, "That's not how we do that now."
**Happily, the same software typically includes a macro that will delete the superfluous spaces. You can put them in, one by one, but your editor can take them all out in a keystroke.