"Hit home" or "hit home on" is an idiom. Its original or basic meaning is "to strike the intended target" as of an arrow or other projectile. But it is used in several metaphoric senses. "His words hit home" means that the words had a significant effect on the listener, that the listener took them to heart. It may imply that this was the intended effect, but it need not.
In the given example:
... the question hit home on a classic example of the English language’s tendency for exceptions.
"hit home" mans that the question in a sense "landed on" the example (which no doubt the text goes on to explain). That is, that one cannot answer the question without exploring the example of an exception, because that example is central to the question.
In this instance, I think that 'hit home" is a less than optimal idiom to express the concept. But it is perfectly valid. I might have written:
... the question directly involves a classic example of the English language’s tendency for exceptions.
The OP asks: "What does the writer mean by "a classic example of the English language’s tendency for exceptions?"
English grammar is notorious for being more a collection of exception than a collection of rules. Few absolute rules exist for English usage to which some exception cannot be found. This is partly due to the changes from Old English to Middle English, and then from Middle to Modern English, which were not made with complete consistency. It is partly due to the tendency of English to appropriate vocabulary, sometimes with accompanying grammatical patterns, from other languages. It is partly due to people who have invented and popularized a number of "rules" for English which are nothing of the sort; which do not and never did reflect actual English usage. (Some of these were based on the assumption that the rules of Latin grammar must also apply to English.) And partly it is just the way English usage has developed.
The quoted expression is referring to this tendency. "tendency for exceptions" might better have been expressed as "tendency to generate exceptions" o0r perhaps as "profusion of exceptions". But then Quora answers are often composed on-the-fly, and may not consist of well-polished prose. (Speaking as one who has posted a good many Quora answers.)
In short "a classic example of the English language’s tendency for exceptions?" means simply a classic example, like many others, of an exception to the widely known rules of English Grammar and usage.
