A turning point is literally a place where things twist direction.
Tips
history
捩 is not a free word in modern Chinese; it survives bound in the literary 转捩点 (turning point), a more formal twin of 转折点. It is the hand radical 扌 plus the phonetic 戾.
register
Literary and bound only; everyday Chinese uses 扭转 for twisting.
戾 gives the sound (lì drifted to liè) and adds a faint flavour of going against the grain — fitting for a forceful twist. It is a dog 犬 under a door 户.