Perhaps the best way to improve combinative skill in practice is to focus on checks, captures and threats on each move whether it’s your move or the opponent’s. This is very easy to read but very hard to put into practice.
The reasons can be different, either poor training or just being too involved with a plan. And if that doesn’t happen, we might have different world champion!
Here is an example taken from one of Artur Yusupov’s books:
Yusupov rejected the move
hg6 – Rxg6
and played Bf4 and game was ended in a draw.
Yet as he himself explained, after Rxg6 he missed Qxg6 (a capture)- fxg6 and now f7, a threat which can’t be met.
For kids and amateurs I can see that poor training is the main cause; most coaches just recommend good tactical books for furnishing enough information on tactical motifs. But I prefer to be with kids while they are solving combinations of tactical exercises and continue hammering home the idea to look for checks, captures and threats on each move.
Another reason is poor chess vision, and the best way to improve in this area to play blindfold games with your partner or coach or to solve exercises without sight of the board.