Caro-Kann c5-c4 push I am having trouble understanding why the push c4 here is incorrect for Black.



After 9. Qc2 b5 10. a4 a6 11. axb5 axb5 12. Rxa8 can be recaptured with the Queen and the pawn chain is stable.

What is wrong then with this push?
c4 is the usual beginner's mistake of releasing the tension unnecessarily. With the pawn on c5 you exert some pressure on d4 which can be increased with moves like Ne7-c6. When the pawn moves to c4 that pressure disappears. 

If you played Ne7 instead then taking the c5 pawn is bad for white. You are not going to retake immediately but instead play Nc6. This gives white the choice between allowing you to recapture on c5 with the bishop with gain of tempo or allowing you to take the more important e5 pawn. Instead of taking on c5 white will want to develop his queenside pieces but this is awkward in the current position. His dark squared bishop is problematic.


  After 9. Qc2 b5 10. a4 a6 11. axb5 axb5 12. Rxa8


This is "hope" chess. You "hope" your opponent is going to make some bad moves and then your bad move magically becomes a good move. If you want to improve then you have to stop doing this. 

Your opponent is not going to play Qc2 because if the c file opens then he wants a rook on that file not the queen. Qe2 is better. He is also not going to play 10. a4. He is going to play 10. b3, immediately attacking the front of your pawn chain.

Furthermore you are a long way behind in development with your king still stuck in the middle. You should not be wasting time on further pawn moves, particularly ones which threaten to open the position leaving your king exposed to attack. Ne7 is more to the point, developing a piece and getting you one move closer to being able to castle.