Help me understand this move?

After my opponent played Nxe5, I played dxe5 instead of fxe5. It turns out dxe5 was a mistake and taking with the f pawn was the best move. In the game, I remember my logic being that if I took with the d pawn, my unprotected knight would be safe from black's rook. Can someone help me understand why taking with the f pawn is such a better move? Thanks

After fxe5 fxe5, you can recapture with the knight (Nxe5) and you won't be left with an isolated pawn (and your knight is not hanging). After dxe5 fxe5, you would have to capture with the knight and while that does not leave the f-pawn hanging, it locks your queen to defend it, which is not optimal. In addition fxe5 undoubles your f-pawns, so you are improving your pawn structure.

Also, you want to attack on the kingside and if you do that, you do not want a counterattack in the center. You want the center to be stable, especially here, where Black has all the pawns on light squares and the Bishop on a6 is just bad. Without that pawn on d4, Black has d4/c5 ideas. You don't want that.

Solid reasoning behind the move, but it actually points to the other capture. You noticed correctly that your king safety is a potential weakness in your position.

One rule to remember: a weakness that can't be attacked, is not really a weakness. In this position, if you take with the f-pawn and you open up the f-file, you will notice that it's only black's rook attacking f2. It can't really be attacked much more. Black has a knight on e8 that is in the way, so the rook on a8 can't easily join. Maybe the queen could join in, but you're still able to easily defend the f-pawn. The f-pawn is therefore not much of a weakness. 

Another thing to remember is that if your opponent has a king stuck in the middle, you want to open up the position. So a strategy for your opponent would be to try and open up the game. In closed positions one would open up the position usually with a pawn break. Here black can't go for ...c5, as it's defended twice and there are very few other pawn breaks. The only pawn break black has is a potential ...a5, but Ba6 is quite in the way. After you took with dxe5, suddenly black gets 2 more pawn breaks: ...c5 and ...d4. You'll notice how much easier it has become for black to open up the position!

There's actually one more point to make. The position is very, very strong for white. The biggest problem for black is that he has no counterplay. He has no plan of his own. You've basically locked up the queenside and the center, forcing black to confront you where you are strongest: on the kingside. Because black is so cramped for space, it's very difficult for him to bring more pieces to the kingside. In positions with a closed center players will try and play on the wings. If you can manage to keep the center closed and lock up the wing where you're not attacking, you'll very likely win the game. So that also points to fxe5 (and after fxe5, Nxe5 occupying the strong square in the center), as you want to try and keep black completely locked up on the queenside and in the center.

I think it is because the d-pawn is better than the f-pawn in its current position, so it should be better to leave the d pawn intact while undoubling the f pawn and connecting it to the pawn chain. 

nice explanation from @RAU4ever, not surprised why he/she is an titled player  thanks for that.

for me, it just fixes your doubled-pawn problem and gets you a good-knight-outpost hehe

after taht Bxg6, hxg6, Qxg6+, Kh8, Nf7 check forks king and queen.. and rook has to take and you lose a knight + a bishop for a rook and 2 pawns (+1) and your queen puts enemy king undersiege..

thing is.. you wont have anything left to support the attack lol.. maybe your h-pawn (and your rook behind it) can join later.. but that would be very slow..