I've seen some websites automatically applying italics on quotes, and when I got a quotes italicized with Korean text, it looked weird on my eyes. Is it just me, or unwritten rules of Korean language, or codified by the Korean Institute not to use them?
I would say it is abnormal to italicize Korean letters for quotation without aesthetical intentions.
In Standard Korean Language Dictionary, 이탤릭체 (italics) is defined as "약간 오른쪽으로 기울어진 모양의 서양 글자체. 주의하여야 할 어구, 외국어, 학명 따위를 나타내는 데 쓴다." 서양 stands for the West, which means italics do not belong to Korean styles. Regarding how to replace the italics, someone already studied the font design quite thoroughly. This book mentions that Korean fonts do not have italics, and it is true: for example, there is Malgun Gothic (Bold, Regular, and Semilight) but there are no such things as Malgun Gothic Italic.
According to 한글 맞춤법 (2017) and 문장 부호 해설 (2014), 큰따옴표 (double quotation marks) should be used to repeat what one (has) said or written; 작은따옴표 (single quotation marks), 드러냄표 (single dots above letters), and 밑줄 (underlines) should be used to emphasize part of a sentence. Single quotation marks are also used to mark the quotation within a quotation and to quote the words from one's mind.
For emphasis, Markdown supports bold and italic types; however, most Koreans will agree that italics are unsuitable for Korean text. Slanted Korean letters usually look ugly and somewhat illegible. For the emphasis, underlines, single quotation marks, and bold letters are usually used in digital writing, since 드러냄표 cannot be typed without custom CSS on the Web. Some people use double quotation marks as well to emphasize part of a sentence, although that is nonstandard for Korean. It seems that StackExchange does not allow the underline tags, so I cannot help relying on italics here when I feel that bold letters look too strong and single quotation marks would not be noticeable.
I have found that
<cite> tags italicize characters and several blogging platforms use those tags for quotation. It is natural that bloggers who cannot use custom CSS do not attempt to change the styles. Fortunately,
this quote is not italicized because it uses
I don't think there's an explicit rule against using italics, but it's rather that there's no rule (or convention) where we do use italics. In other words, italics have no established place in Korean, and using them would be considered a "special effect" similar to using, say, Fraktur font in English. (Also, it's subjective, but I do think Korean in italic font looks ugly.)
I will explain several major roles italics play in English writing, and how you can achieve similar effect in Korean.
Change of meaning via emphasis
For example, consider these English sentences:
I did not purchase the book.
I did not purchase the book. (Someone else did.)
I did not purchase the book. (It was a gift.)
In speech, you can emphasize some words and change meaning. Because they still contain an identical list of words, in English writing it is indicated by italics. In Korean, such an effect is usually achieved by using different suffixes and/or word order. So they can be rendered as:
그 책을 안 샀어요.
저는 그 책 안 샀어요 / 그 책을 산 건 제가 아니에요.
그 책을 사지는 않았어요 / (제가) 그 책을 산 건 아니에요.
Even though I showed some words in bold (these words will be emphasized in speech), in writing usually there's no need for them: the sentence structure (and context) will make it clear what is being emphasized.
Some less obvious examples I can think of:
What a great person! = 참 훌륭한 분이네!
What a great person! (sarcastic) = (어이구) 훌륭하시기도 하셔라!
I said, "when are we arriving?" = 언제 도착하냐고 했어요.
I said, "when are we arriving?" (annoyed) = 언제 도착하냐고 했잖아요.
Clearly, Korean has no concept of italics-as-quotes. So you will commonly use double quotes for actual speech and single quotes for thoughts.
Sometimes people just get rid of quotation marks and achieve a similar effect as English quotation, but I'm not sure if that's considered "standard". For example:
어머니는 다시 비누질을 하며, 대체 그대는 매일 어딜 그렇게 가는 겐가, 하고 그런 것을 생각하여 본다.
(박태원, 소설가 구보씨의 일일, 1934)
There's no hard line between this and the first set of examples, but sometimes you just want to emphasize a word or phrase. In English, you can use CAPITALIZATION, italics, and sometimes bodface. In Korean, you would commonly use boldface or underlines.
In traditional orthography rules, there's also 드러냄표, which is putting a single dot on top of each letter. It looks very nice with Hangul. Random example from the web:
Unfortunately they aren't supported in most softwares, so they have fallen out of favor these days.