When quoting an author you are not supposed to change their grammar mistakes...why?

As already indicted, a quote is a quote, and it should be what its author wrote. There are exceptions.

1. When a person is speaking without notes or writing a draft, then what you hear or read is not a finished work, and it is considered simple courtesy to correct errors that the author would not make in a finished text. For example, a person begins "Last week I...", stops and begins again, "When I was in Tulsa last week..." There is simply no good reason to include the first sentence fragment. Your objective is to report what was worth repeating. You are not a court reporter recording every word.

2. Languages differ. Even English differs from country to country and from region to region. When a British speaker speaks of "being knocked up this morning," she conveys a very different message to her Briish audience than to Americans reading an account in their newspaper. A good reporter in this case would paraphrase: "The poet had just been awakened in her hotel room when..."

3. Spelling is not as standardized as persons think. A "misspelled" word may simply reflect a different background. The American who writes 'catalog' has not spelled 'catalogue' wrong. He is just conforming to American usage. An American President of the early 19th century once wrote: "I have nothing but contempt for a person who knows only one way to spell a word." When an English reporter records an American's poem, has he any way of knowing if the bird was 'gray' or 'grey'? It is wisest to write using the spelling your audience would expect. Omit the [sic].

4. Grammar is not standardized either. A modern writer may split infinitives in defiance of older, Latin-based, rules of grammar. Older writers wince when they hear such 'abuse.' In such cases, report what you hear. Do the same with improper antecedents and dangling participles. "Having eaten our lunch, the steamboat departed" is bad English, but you can't correct it without paraphrasing, and a [sic] only points out what can be ignored. Who cares if the steamboat was hungry?

5. We routinely modernize older authors. While we may retain the archaic language of the King James Bible, most prose from the period is improved by using modern spelling. Tell the reader what you are doing and proceed with a clear conscience. Don't tamper with poetry. Too much thought went into the original words.

Well nothing would really happen, it just wouldn't technically be correctly quoted. The reason you aren't supposed to change things in the quote, even grammar mistakes, is because that changes what the quote originally was, and therefore you are, in a way, putting it into your own words, but you are putting quotes around it. But you also can't just leave the quotes out because that is plagiarism.

That might be how the author intended it to be so if you want to quote their saying and they used grammatical errors and you happen to change it your no longer quoting them because that was not their intentions in the sentence or quote, so unless you don't want to quote someone you should use their grammatical errors too. Also some might interpret someones words and say their grammatical errors meanwhile that might just be how the language was in that time in age for example Shakespeare so it would ruin the quote my changing their grammar and one might not get the authors intentions of what they meant the sentence to be. Hope I helped.

I you make any changes to a quotation you are no longer quoting; you are paraphrasing. Part of the purpose in quoting is to show exactly what is said. To change it, takes away the essence of the quoter. Sometimes the grammar mistake is the soul of the quote.

If you did, it so wouldn't be a quote!