Puzzle Analysis HGnwZ

I often initially think the computer is mistaken until I play around with my moves and find the fault is entirely mine. However, there are puzzles where I cannot find a fault in my move which I believe to be superior to the computer.
For instance: lichess.org/training/HGnwZ

Why is rook to b7 inferior to rook to f6?

My proposed move leaves as far I can see 4 options:
Queen takes queen in which case I take rook with rook and check, he can block with queen and Bishop but it will end in mate.
Rook takes rook and Queen takes queen and check mate.
Bishop to e7 which I would counter with queen takes bishop and it will end similarly to option 1.
He could also move the h pawn to avoid check mate but even this seems a more preferable outcome than what the computer says is the best move.

What am I missing here?

The point of Rf6 is that gxf6 is not possible because of the mate threat. The bishop can be taken for free.

There are lots of good replies to your move, because it's not forcing.

Rd8. Qd8. Bd4+.

Bd4 makes a lot of sense actually, you are right.

I think the main problem I have with the puzzles is that it's sometimes very unclear why a certain move is best. It sometimes becomes apparent 3 moves after the puzzle is complete. And sometimes the computer just plays in a way a human would not, for instance sacrificing pieces just to avoid check mate for as many turns as possible. I personally would hope the opponent wouldn't notice and not attract attention towards my own potential doom.

You're right. LiChess doesn't seem to make any attempt to play human looking moves in their puzzles.

I've done over 10K puzzles on sites that do and they have their own downsides. Lots of people arguing about what moves are human looking. Lots of puzzles where horrible moves are played in the middle of puzzles. For example doing mating puzzles where there's no forced mate can be frustrating. At the start of a puzzle you look for something that's not there.

I tend to stick to the ones with set tasks (mates in 3/4) to avoid such potential ambiguities.