Picture a long road with a house standing at its middle point. You are not at the place you left, and you are not at the place you are going; you are at the one building between them, and you will move on. Everything this phrase does comes out of that position. A resident of a halfway house has left the institution and not yet reached their own front door. A halfway-house policy has left the old rule and not yet reached the new one. In every use, the meaning is not what the place is, but where it stands — in the middle, on the way to somewhere else.
From the word’s history
Wiktionary notes that the literal sense — an inn about midway along a journey — was already a well-established term when Samuel Pepys mentioned a famous example in his diary in 1662. So the road-and-house picture is not a later metaphor; it is where the phrase started.
Wiktionary 指出，字面的意思（旅途中間那間客棧）在培普斯（Samuel Pepys）一六六二年的日記提到一間有名的 Halfway House 時，就已經是通行的說法了。所以「路中間那棟房子」不是後來才生出的比喻，而是這個詞一開始的樣子。
Wiktionary (kaikki extract) entry for halfway house, etymology_text citing Samuel Pepys's diary, 1662 [source_ref kaikki:3f6f69a190036ae4:1884427206]
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