Do you mean f4?
e6 and f6
No, I mean f6, the most recent place I've heard it was this agadmator video. https://www.youtube.com/watch?v=C17wrLYb30o at the 6:35 mark.
I know this isn't the only place I've heard it. This is just the one that made me wonder about it.
the answer is in your question. e6 is not a natural square for a knight. in fact it would take a few moves to get it there. Pushing e6 doesn't prevent castling as blacks bishop controls the diagonal. if black pushes f6 then the white bishop can come to c4 and prevent castling. c4 is a natural square for whites kingside bishop. Set up a board and shuffle the pieces round and you will see how troublesome an early f6 can be for blacks development.

The reason c6 is usually a much better move than f6 is that c6 doesn't open a diagonal towards Black's King. It is true that putting a pawn on c6 takes away that square from Black's Knight but the benefits Black gets in return often outweigh this slight drawback. For example c6 opens a diagonal for Black to develop their Queen and c6 can also be useful for reinforcing the center.
if you push to c6 you can always develop the knight to d7 where it can also reinforce e5. just be aware the yo
I keep hearing about f6 being a bad move (in general) with blocking natural knight development and weakening the kingside in the case of a castle, but I never hear this with an e6 move. Isn't this just the same case except on the other side of the board?