a catch or snag; something that catches or holds (physically), or a point where something gets stuck.
コートのボタンがバッグに引っ掛かり、糸がほつれた。
A coat button got caught on the bag and the thread came loose.
チェーンに引っ掛かりがあって、自転車の車輪が回りにくい。
There's a snag in the chain, so the bike wheel doesn't turn smoothly.
その金具の引っ掛かりで扉が固定される仕組みだ。
The door is held in place by that catch on the fitting.
a connection or link; a trace of relation between things or people (often implying some involvement or tie).
警察は事件と彼の過去の仕事との引っ掛かりを調べている。
The police are investigating a link between the crime and his past job.
この企業と政治家の間には微妙な引っ掛かりがあると報じられた。
It was reported that there is a subtle connection between the company and the politician.
a feeling of unease or discomfort; something that nags at you emotionally or mentally.
彼の言い方にどうしても引っ掛かりが残った。
His way of speaking left me with an uneasy feeling.
説明を聞いたが、どこかに引っ掛かりがあって納得できない。
I heard the explanation, but something still bothers me and I can't accept it.