why is this move best move ??


Black is doing well after either move I think. 'A weakness is only a weakness if it can be attacked'. After gxf4 can you explain how white will be attacking the black king?

pawn g2 to g4, queen swing to king side, bring up rook, or pawn g4-g5, then pawn f5 push down f6 threatening entire king area ??


pawn g2 to g4, queen swing to king side, bring up rook, or pawn g4-g5, then pawn f5 push down f6 threatening entire king area ??
This is quite vague...in such a position you have to try to analyse the specifics. Let's see:
For example. Black can cover everything comfortably if white trys invading on the kingside. In fact all white has done is make his own king weaker.

Ohhhh, I forgot about the enpant something capture move from pawn . That might make sense
with that, white pawns can't connect and can't be a threat.
Black is being attacked from the queenside.
If exf4,then black exposes the base of his pawn chain to white's bishop. Black would also be splitting his pawn island.

En passent. Yes, even without that though black has other resources if white goes g4.
Example lines with limited analysis by me. The entire central construction for black is extremely strong and this is why gxf4 is better than exf4 - it makes it even stronger. If white could get real counterplay against the black king it might be a different story, but given that white cannot do anything really to attack the black king there is nothing to fear from playing gxf4.