I am really confused by this one. In response to ...Bb4 the "correct" response is Bd2. Nb2 is "wrong", not even "good move, but you have a better". Yet, I preferred to keep both bishops and Nb2 can accomplish this, unless black prefers capturing either a bishop and a knight, or two knights, to capturing a rook and a knight.
I know I must be missing something here, but I studied it for a long time and I just can not find the problem with Nb2.
In puzzle number 47569 2.Nb2 is not a legal move because the white king is in check! Perhaps you mean 2.Nd2? If so, then black can play 2...Bd2+ followed by 3.Bxd2 Qe5+ and the black queen escapes with check and black now has the advantage!
Sorry, not able to tell b's from d's. What I was trying to say was:
1Na4...Bb4
2Nd2 (instead of Bd2),,,Bxd2
3Kxd2...Qxa1 (there are other responses, but all of them are worse for black than Qxa1)
4Qxa1 (this leaves white with 2 bishops)
After 2.Bd2! white's knight still defends the pawn on e5. Your move 2.Nd2?? allows the trapped queen to escape after 2...Bxd2+ 3.Bxd2 Qe5+!
If 1.Na4 Bb4+ 2.Nd2?? Bxd2 3.Kxd2 then white is significantly worse after 3...Qxe5 because white has allowed the black queen to escape and white has also lost his castling rights and has to worry about his king safety.
During the middle game, the king is generally safer on the edge of the board rather than the middle of the board. The king is best protected behind a row of pawns, which is why most players choose to castle. Your idea of 3.Kxd2?? gives up the castling rights for white and unnecessarily exposes the white king to attack.
When the pieces are tied down to the defense of the king you will have fewer options to attack your opponent. Instead of 3.Kxd2?? Qxe5, preferable is 3. Bd2 Qxe5+ 4.Be2 because white then preserves his castling rights, which after castling, will keeps his king much safer from his opponent's threats.
I hope my explanation is clear enough to understand.