Whilst the number of tactical themes may be finite, it's not a small number. Plus, you get combinations of tactical themes such as a removal of the guard exploiting a pin forcing a move that leads to another tatcical position.
As the levels of difficulty increase, you need to be increasingly accurate - the problems will be higher rated as many fail them. One of the main reasons for people failing the problems is that a move that looks winning has a cunning defence and, whilst the idea is correct, only 1 of several moves both continues the threat and defends against the refutation (a perpetual check for the defending side etc).
Then you have to take into account that these accurate moves need to be found not just on move 1 but sometimes for 5 or 6 consecutive moves against slippery defences. "Quiet moves" - ones that don't immediately check or capture but perhaps prevent a defence are often missed and these will cause the problems to be rated higher too.
It sounds like you've made excellent progress with your tactics training already - keep going!
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You will see layers of tactics, with red herrings that look like good moves, but actually lead to subtle disasters.