Why is 6. a3 a mistake compared to Qa4+? I played a game on lichess recently. Afterwards, I used the analysis feature, including the "learn from your mistakes" feature, and it said that 6. a3 by white was a mistake, with 6. Qa4+ as best. I'd like to know why, as I don't understand why 6. Qa4+ is superior.

[After Qa4+ , it seems to me black can play 6. Nc6, and if the white queen captures the black knight, 7. Qxc6, it seems to lead to a draw as the white queen cannot escape capture threats starting with 7. Bd7 by black.]

   [FEN ""]

   1. d4 d5 2. e3 { D00 Queen's Pawn Game } a6 3. c4 b6?! { (0.12 ? 1.07) Inaccuracy. Best move was e6. } (3... e6 4. Nf3 c5 5. cxd5 exd5 6. Nc3 Nf6 7. Bd3 c4 8. Bc2) 4. Nc3?! { (1.07 ? 0.50) Inaccuracy. Best move was cxd5. } (4. cxd5 Nf6 5. Nf3 Bb7 6. Be2 Qxd5 7. Nc3 Qd6 8. O-O Nbd7 9. Nd2 e5 10. Bf3 c6) 4... e6 5. Nf3 Bb4? { (0.17 ? 1.63) Mistake. Best move was Bb7. } (5... Bb7 6. b3 Nf6 7. Bb2 Bd6 8. Bd3 O-O 9. O-O Nbd7 10. h3 c5 11. cxd5 exd5 12. Ne2) 6. a3? { (1.63 ? 0.59) Mistake. Best move was Qa4+. } (6. Qa4+ Nc6) 6... Bxc3+ 7. bxc3 f6?! { (0.65 ? 1.60) Inaccuracy. Best move was Nf6. } (7... Nf6 8. cxd5 exd5 9. Be2 Nbd7 10. O-O O-O 11. a4 c5 12. c4 Bb7 13. Bb2 Rc8 14. Nd2) 8. Qc2 g6 9. cxd5 exd5 10. c4 Ne7?! { (1.74 ? 2.43) Inaccuracy. Best move was Bf5. } (10... Bf5 11. Bd3) 11. cxd5 Qxd5 12. e4?! { (2.47 ? 1.93) Inaccuracy. Best move was Bc4. } (12. Bc4 Qd6 13. O-O Be6 14. d5 Bf7 15. Rd1 b5 16. Ba2 Nd7 17. e4 O-O 18. Be3 g5) 12... Qd6 13. Be2 Bg4? { (2.31 ? 3.33) Mistake. Best move was Bb7. } (13... Bb7) 14. Bb2?! { (3.33 ? 2.57) Inaccuracy. Best move was O-O. } (14. O-O Nd7 15. Rd1 h5 16. h3 Bxf3 17. Bxf3 Kf7 18. a4 Qc6 19. Qd3 Qe6 20. Bf4 c6) 14... Nbc6?! { (2.57 ? 3.07) Inaccuracy. Best move was Nd7. } (14... Nd7 15. O-O O-O 16. Rfd1 c6 17. a4 Rfe8 18. Ba3 Qb8 19. Qb3+ Kh8 20. Bc4 Kg7 21. Bf7) 15. d5? { (3.07 ? 1.98) Mistake. Best move was O-O. } (15. O-O) 15... Bxf3 16. Bxf3 Ne5 17. Be2 b5 18. O-O O-O 19. Bd4 Rac8?! { (2.29 ? 3.12) Inaccuracy. Best move was f5. } (19... f5 20. Bc5 Qd7 21. Rfd1 Nf7 22. exf5 gxf5 23. d6 cxd6 24. Qb3 d5 25. Qg3+ Ng6 26. Bxf8) 20. f4? { (3.12 ? 1.35) Mistake. Best move was Bc5. } (20. Bc5 Qd7) 20... Nc4? { (1.35 ? 3.56) Mistake. Best move was Nd7. } (20... Nd7) 21. Bxc4 bxc4 22. Qxc4 c5 23. Be3 Kg7? { (3.59 ? 4.87) Mistake. Best move was f5. } (23... f5 24. Rac1 fxe4 25. Bxc5 Qxd5 26. Qxd5+ Nxd5 27. Bxf8 Rxf8 28. g3 Nf6 29. Rc6 a5 30. Ra6) 24. Rac1 f5? { (4.67 ? 6.59) Mistake. Best move was Qd7. } (24... Qd7 25. Bxc5 a5 26. Qc3 a4 27. Qd4 Rfd8 28. Rc4 Qe8 29. Rfc1 Qf7 30. Rxa4 Nxd5 31. exd5) 25. Bxc5 Rxc5?! { (5.89 ? 6.59) Inaccuracy. Best move was Qd7. } (25... Qd7 26. Qc3+) 26. Qxc5 Qxc5+ 27. Rxc5 fxe4 28. d6 Nf5 29. d7 Rd8 30. Rd1 e3 31. Kf1 Ne7?! { (6.49 ? 7.39) Inaccuracy. Best move was Kf8. } (31... Kf8 32. Ke2 Nh6 33. Ra5 Ke7 34. Rxa6 Ng4 35. a4 Nf2 36. Rd4 Ng4 37. h3 Nf6 38. Kxe3) 32. Ke2 Nf5? { (7.22 ? Mate in 10) Checkmate is now unavoidable. Best move was Kf7. } (32... Kf7 33. g4 a5 34. a4 h5 35. gxh5 gxh5 36. Rxa5 Ng6 37. Kxe3 h4 38. Rad5 Ke7 39. a5) 33. Rc8 Rxd7?! { (24.96 ? Mate in 8) Checkmate is now unavoidable. Best move was Kh6. } (33... Kh6) 34. Rxd7+ Kf6 35. Rc6+ Nd6 36. Rcxd6+?! { (Mate in 2 ? Mate in 2) Not the best checkmate sequence. Best move was g4. } (36. g4 a5 37. Rcxd6#) 36... Kf5 37. Kxe3?! { (Mate in 2 ? Mate in 4) Not the best checkmate sequence. Best move was Kf3. } (37. Kf3 g5 38. Rf7#) 37... Kg4 38. Rxh7 g5 39. fxg5?! { (Mate in 3 ? Mate in 4) Not the best checkmate sequence. Best move was Ke4. } (39. Ke4 a5 40. Rg6 a4 41. Rxg5#) 39... Kxg5 40. Rc7 Kf5 41. Rc5+ Kg4 42. Rd4# { White wins by checkmate. } 1-0 *
In short: Qa4 forces black to lose grip over central light squares as black is tactically being restricted to recapturing with a queen on d5 instead of a pawn, leading to:

As opposed to any of the actually desirable and common setups for black, which might look like: (with Nf6 instead of Bb4, and quick Bb7 and castling being prioritized)



It helps to try and understand the purpose of every move at a basic level, let's start with your 3rd move c4: Clearly, one of the most common and signature moves of all queen's pawn games, but what purpose does it serve?
Openings are a lot about taking control over the centre and not conceding it easily to your opponent, so when white plays 1.d4, they're claiming control over dark squares, namely e5 and c5, similarly, black replying with 1...d5 they're reciprocating by controlling c4 and e4 (so light square control). And that brings us to the famous c4 move, which attempts to undermine black's control over light square, so whenever white manages to force black's hands into either taking on c4 or recapturing on d5 with a non-pawn piece, you could say white has achieved a small success in central control, which among other options may allow white to play e3-e4-e5 and take away more squares from black's minor pieces. These ideas should make it a bit more intuitive as to why, black recapturing with a non-pawn ought to be a strategic gain for white. Let's summarise with a diagram, in blue the desired central setup with d4-e4, and the green c4 the enabler, and in turn black's intends to keep maintain grip over d5 with e6/c6.

Now let's have a closer look at your game: 5...Bb4 by black is a terribly odd and poor move: black is playing rather inconsistently, first opting for an early queen-side development with b6 to fianchetto their c8 bishop, but then develop their dark squared bishop, temporarily ignoring the created light square weaknesses, in particular c6. Moreover, bishop developments before knights are possible but rather rare, in general knights are more easily developed (as their restricted movement makes their optimal development easier to resolve given a structure), and they in turn create useful space for the bishops. And your game makes for a perfect example of such careless development as it can be tactically exploited with an immediate Qa4+ which:

Forces Nc6, which is not only a non-ideal knight placement in this position (the structure tends to favour developments of the type Nd7-Bb7-Nf6-Be7 with an early c5 to challenge white's centre, impossible with a knight on c6) but it also allows white to force a queen recapture on d5 after cxd5.
After 7.cxd5, black can either take on c3 first with check, or take on d5 with Qxd5 immediately as the knight on c3 is pinned. Obviously, exd5 is not a choice as it outright blunders c6 since the queen will no longer be caged as it can take on d5 afterwards.
Not only white will have fully claimed the centre, but they will also be much ahead in development and black has a real struggle ahead to even meaningfully finish development (no prospect for active knights, open files and rook activity ...) while parrying white's upcoming threats, to showcase with one possible scenario, after 7...Qxd5 8.Bd3 Ne7 9.O-O Bxc3 10.bxc3 O-O 11.e4 Qd8 we reach the following position:


Note that black conceding the d5 pawn with either dxc4 or a non-pawn recapture would be acceptable provided they could maintain sufficient light square control with their minor pieces afterwards, e.g. a knight on f6 and a fiachetto'ed b7 bishop. The latter may further justify the opening of the long diagonal for creating active play against white's king.
Last but no least, at a rough basic level similar to our earlier discussions, there are openings where black even encourages white towards an early advancement of central pawns, which black aims to exploit by either fixing the structure and therefore inducing a weakness (like the King's Indian Defence) or by actively trying to undermine the central structure in order to create a weakened target (such as the Grünfeld Defence), all backed by an early kingside development.