Why Nc3 instead of Nf6?

Well, Nc3 is the Vienna Game, and can be played many ways. One idea is to go for a delayed sort of king's gambit with f4 on the next move as an attempt to improve the original gambit.

2. Nf3 attacks a pawn, but 2. ... Nc6 defends it no problem. On the other hand playing f4 is the start of a long term attacking plan. 2. f4 is really attacking. 2. Nc3 and 3. f4 is also very attacking and obviously 2. Nf3 and 3. f4 is not possible.
There's also a pretty interesting line that starts: 1.e4 e5 2.Nc3 Nf6 3.Bc4 Nxe4 (after 4.Nxe4 d5, Black wins the piece back) 4.Qh5. I forget the whole line, but it's called the Frankenstein-Dracula Variation and it's very cool in my opinion :) (google it if you need to). Pretty much, White creates one mating threat after another, while Black is forced to defend. Black ends up down the exchange, but with a development advantage and the possibility of trapping White's vulnerable Queen.

Tartakower: The strength of this move, paradoxically, is that it threatens nothing.
And what Paulgottlieb said, White wants to get in f4 before nf3.

Because Nc3 does not block the f pawn.