Looking for a defense against 1.d4 I wanted to learn a good opening against 1.d4 that does not involve the second move being 1...d5. I personally don't like symmetric positions very much. To give you an idea of the type of openings I play right now, for white, I play Catalan and I play French against 1. e4. Anyone have any ideas for responses I should look into?
I suggest c5. As commented by @NoseKnowsAll it is called the Old Benoni Defense. If white is a pro they will probably have an edge because of their experience but generally, for your criteria (it is not symmetrical) it has the highest statistics for black winning in some of the databases such as https://www.365chess.com/opening.php?m=2&amp;n=7&amp;ms=d4&amp;ns=7.
Note that it is moderately common (+16k games in the database cited above) which makes the statistics more meaningful than some uncommon moves like a5.