-아/어야 하다
-a/eoya hada
Not because you want to — because it's been set on you
The picture Someone has set a stone on your shoulder. You move because of the weight. Only the identity of whoever set it there changes. -야 하다 is a stone set on you from outside; -고 싶다 is a hand pulling you from inside. Same action — pushed into it, or drawn toward it.
Where the picture shows up in -아/어야 하다
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a deadline set it there
내일까지 보고서를 내야 해요.
nae-il-kka-ji bo-go-seo-reul nae-ya hae-yo
I have to turn the report in by tomorrow.
Tomorrow's date, circled on the calendar, turning into a stone on your shoulder.
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a rule set it there
여기서는 신발을 벗어야 해요.
yeo-gi-seo-neun sin-ba-reul beo-seo-ya hae-yo
You have to take your shoes off here.
The shoes-off notice at the entrance turning into a stone that presses on your shoulder.
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your body set it there
약을 하루 세 번 먹어야 해요.
ya-geul ha-ru se beon meo-geo-ya hae-yo
I have to take the medicine three times a day.
Three medicine packets lined up over one day, pressing down on your body.
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the lighter, spoken stone
지금 출발해야 돼요.
ji-geum chul-bal-hae-ya dwae-yo
I have to get going now.
The stone on your shoulder shrinks a little, and the words come out lighter.
-야 돼요 is the everyday spoken version and sounds a touch lighter.
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a goal set it there
합격하려면 매일 공부해야 해요.
hap-gyeo-ka-ryeo-myeon mae-il gong-bu-hae-ya hae-yo
If I want to pass, I have to study every day.
A goal hung far ahead on a rope, tugging your shoulder a little every day.
Paired with -려면, the stone is the one your own goal put there.
All of it in one picture
-야 하다 is one stone set on your shoulder. When the circled date on the calendar becomes the stone, it is a deadline; when the notice at the entrance becomes it, a rule; when three medicine packets sit on one day, your body's orders; when the stone shrinks a little, the easier spoken -야 돼; when a goal hangs ahead on a rope and tugs, daily study. In none of these does your own wish put the stone there. That is why saying -야 하다 always tells the listener the task came from outside you, not from wanting it.