Recently I played a chess game that started with the moves: 1. e4 e6 2. d4 a6 and then I played 3. c4 which according to Stockfish is inaccurate.
[fen ""]
1. e4 e6 2. d4 a6 3. c4
What is the reason for that? How is this situation any different in essence from the King Indian defense for instance in which White occupies the center right away with 1. d4 Nf6 2.c4 g6 3. Nc3 Bg7 4. e4 ... ?
[fen ""]
1. d4 Nf6 2.c4 g6 3. Nc3 Bg7 4. e4
When comparing two lines with the help of the engine, it often helps to play around with the moves by switching them between different lines and analyze the difference.
Compare for example
.
[fen ""]
1. e4 e6 2. d4 a6 3. c4 d5 4. Nc3 (4. exd5) dxe4 5. Nxe4 Bb4+ 6. Nc3
and
.
[fen ""]
1. e4 e6 2. d4 a6 3. Nc3 d5 4. Nf3 dxe4 5. Nxe4 Bb4+ 6. c3
In the first line, 5...Bb4+ is nasty, White is basically forced to block that check by 6. Nc3 (d4 is undefended after 6. Bd2 and the c-pawn is obviously missing, too).
In the second line, 6. c3 is an easy answer to 5...Bb4+.
Conclusion: Playing c4 first makes playing Nc3 more tricky. In fact, Stockfish instead suggests 4. exd5 as the best continuation in the first line. But does White really want to capture right away (instead of developing the other knight like in the fourth move of the second line - never mind that he still has not developed the first one)?
It's not inaccurate whatsoever. 3.c4 is just as good a move as 3.Nf3, 3.Nc3, etc. In general you should take what engines say that early on with a grain of salt, unless the position is already extremely tactical. What was the evaluation drop when you played 3.c4, and what depth was Stockfish thinking at? For me, at depth 27 Stockfish 10 goes down from 0.58ish to 0.48ish, which isn't significant on move 3.
2.c4 is generally considered the best way to take control of the center after 1.d4 Nf6, since 2.e4 is no longer possible, but after 1.e4 e6 2.d4 a6 White already has the ideal central Pawn formation e4-d4, and has no need or hurry to push another Pawn to control the d5 square with c2-c4. He can simply begin developing some pieces instead. Of course 3.c4 is no terrible mistake, but I'd go for development with either Nc3, Nf3, or Bd3, keeping an eye on the center with my pieces.
First, I would not trust the engine in a position where not that much is happening. It has no clue what it's talking about. If you are going to trust it anyway, at least try to see what the answer to your "inaccurate move" is suggested to be.
But I think it's kind of right in this case: 3.c4 appears to fight for the center, but I'd say it makes your fight for the center more difficult. Compare for instance 3.Nf3 d5?! 4. e5! with the lines given by Annatar, where it's not a good idea for White to play e5.
White could here take a chance to develop its pieces, probably with 3.Nf3. If ...b5 is no threat, 3.Nc3 would also be OK. 3.Be3 and 3.Bd3 are fine but a bit more "committing". Flexibility is probably another reason against 3.c4 (you won't be able to take the pawn backwards, so your queenside will remain a bit weaker)
If you check your King's Indian example, most engines will probably suggest 2.Nf3 (or even 2.Nc3!?) rather than 2.c4 unless they are using an opening book (engines have had a "pro-development-bias" for decades). I'd like to add that the situation is indeed quite different as the oppponent's dark-squared bishop will not go to b4, for instance, as in the lines by Annatar, so one of the main inconvenientes of playing c4 is not anymore.
As a final remark on general opening principles (which only partially applies to this case), please try to differenciate between central control and an overextended center. Just because we have a lot of pawns in it, it doesn't mean we are winning the fight for the center. You may want to have a look at some Black victories in the Grünfeld's main-line or the Four pawns attack for some illustrative games
