안/못
an/mot
Who built the wall — you or someone else?
The picture A wall stands across your path. All that changes is whether you built it yourself or someone else did. 안 and 못 are a wall thrown up right before the verb; -지 않다 and -지 못하다 let the sentence stand and flip it at the end. Same builder — different spot on the road.
Where the picture shows up in 안/못
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a wall you built
저는 고기를 안 먹어요.
jeo-neun go-gi-reul an meo-geo-yo
I don't eat meat.
A plate of meat in front of you, with a wall of bricks you laid there yourself.
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a wall built by circumstances
차가 막혀서 못 갔어요.
cha-ga ma-kyeo-seo mot ga-sseo-yo
I couldn't make it — traffic.
Cars backed up down the road you meant to take, standing across it like a wall.
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a wall built by ability
저는 수영을 못 해요.
jeo-neun su-yeong-eul mot hae-yo
I can't swim.
You at the water's edge, with a pane of glass standing between you and the water.
수영 안 해요 means you can swim but choose not to. A completely different sentence.
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insisting you built no wall
일부러 안 한 거 아니에요.
il-bu-reo an han geo a-ni-e-yo
I didn't skip it on purpose.
Holding both palms open to show there is no brick in your hands.
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a wall built by the rules
여기서는 사진을 못 찍어요.
yeo-gi-seo-neun sa-ji-neul mot jji-geo-yo
You can't take photos here.
You raise the camera and a no-photography sign cuts across in front of you like a wall.
A rule is someone else's wall, so it takes 못.
All of it in one picture
안 and 못 are the same wall standing in your path. Lay the bricks yourself in front of the meat and you do not eat it; let a line of cars become the wall and you could not go; let a pane of glass stand between you and the water and you cannot swim; let a sign cut across and you cannot take the photo. And where you open your palms to say there was no brick in your hands, 안 comes back. So the question is never whether there is a wall, but who put it there.