I can't understand why the engine says bc3 is a blunder? Can someone explain why Nc3 better than bc3? Thanks.
Why bc3 move a blunder?
The engines don't tell you the why, but show the what.
For us mortals, we ask things. Like why is the Black queen wondwring around in rough neighborhoods all alone? How, or will she ever return home alive? If so, how will she do it? All this while on her return trip, what does White do?
After 9...Qxb2
White has (in addition to the queen and a knight) developed both bishops and advanced 4 pawns.
Black.has gone for a pawn picking and advanced 1 pawn 1 square.
With the knight on b1 (bishop on c3), the queen gets 1 extra move to eacape from a rook attacking her on the b-file.
Here's a snapshot of what might can happen after a few moves. Pay attention to all of the arrows also.

and here's a little deeper engine thought...
My take on it is that it is more of a mistake than a blunder. If you assess the mistake along with the fact black is underdeveloped, just putting on their dancing queen shoes, it could equal a blunder.
There seems to be a common problem in early stages of the game lower level players miss. That is to play the lesser evaluated piece at all times because we think that will bring about the least damage. Also, we often gloss over anything that attacks a queen. But an open file for the rook can prove to be more advantageous (but not contagious unfortunately, so you have to "rook everywhere", get it? I made a stupid joke). Ok, let's look everywhere.