koreangrumblings:

거리가 있다 (멀다), literally meaning “there is a distance” or “the distance is far”, is an expression that carries with it different connotations depending on the context in which it is used.

저는 유행과 거리가 먼 사람이에요.  Here the expression is used to show that the speaker has a lack of interest in trends.  I’m someone who’s not interested in the latest trends.

안정된 노후생활은 서민들과는 거리가 먼 이야기가 되어 버렸다.  In this second example, 거리가 멀다 indicates that the idea of a stable retirement has become a distant hope for ordinary people.  A stable retirement has grown out of the realm of possibility for everyday people.

그 둘 사이에는 거리가 좀 있어요. 지난 번에 승진하는 일로 싸웠거든요.  In this final example, the expression is used to indicate that the relationship between two people has gone sour.  From my own experience, this seems to be the most common usage.  The two of them are a bit distant with each other.  They fought over the last promotion.

Here are a few more examples from 건국대학교 한국어 4:

내 동생은 다정한 성격과는 거리가 있다.  My younger sibling is not affectionate.

드라마에 나오는 이야기는 현실과는 거리가 좀 멀지요!  Dramas are nothing like real life, are they!

제 음악은 대중들이 좋아하는 음악과는 거리가 있어서 사람들이 잘 이해하지 못하더라고요. My music is a far cry from the music that’s popular among the masses, so people didn’t get it.