Computer says this is a better move than.....but why?

https://www.chess.com/a/26Ny82SVccoCi

I don't see why 3. ...f6 is a worse move than the suggested ...Bd6.

That risks a bishop for bishop trade while the former move actually could still take bishop if he were to move in on black's back rank and instead ...f6 sets up the follow pawn advancement that pushes the white bishop back further. Am I missing something or is the computer not able to think that way?

The computer is programmed to do certain things that have been shown to lead to a good game.

Developing pieces is highly valued in openings, rather than trying to push opponent's pieces back with pawns. The main drawback to 3..f6 is that it takes away the place your knight wants to go. Also, it weakens your king's safety.

I recommend you take some of the lessons here to understand these basic concepts.

Perhaps it would be a good idea to look at Discovering Chess Openings, a book about opening principles.
https://web.archive.org/web/20140627114655/http://www.chesscafe.com/text/hansen91.pdf

Moving f6 at this stage is a really risky move. It exposes your king because the e8-h5 diagonal now open. The white queen may move to h5 at some point and deliver check.

Yeah, basically the board is not symmetrical i.e. there's a kingside and a queenside. Moving the c pawn in the opening is common. Moving the f pawn in the opening weakens the king though, and it's bad in so many positions that beginners are usually told to never do it.

The move … f6 is typically bad, but I'm not sure that it's such a bad move in THIS position.

In an OPEN position it is a very poor move, but here the game is still pretty closed, minimizing the drawbacks of the move. It pretty well commits Black to playing a Hedgehog formation, though.