これは、ビショップが同じ色のマスにある駒しか攻撃できないためである。

N×Nのチェス盤にN個のビショップを互いに脅かさずに置くには、交互に色を変えて置かなければならない。例えば、盤面が8×8の場合、ビショップはある色のマスに、他のビショップは他の色のマスに置くことができる。この場合、一方の色のビショップを4枚、もう一方の色のビショップを4枚、合計8枚のビショップを置くことができる。

つまり、ビショップを交互に配置することで、ビショップ同士の攻防を避けることができるのだ。
The maximum number of bishops that can be placed on an N by N chessboard such that no two bishops threaten each other is N. This is because bishops can only attack pieces that are on squares of the same color.

In order to place N bishops on an N by N chessboard without them threatening each other, they must be placed on alternating colors. For example, if the board is 8 by 8, then bishops can be placed on squares of one color and the other bishops can be placed on squares of the other color. In this case, you would be able to place 4 bishops of one color and 4 bishops of the other color, for a total of 8 bishops.

Therefore, the reasoning behind this arrangement is that by placing bishops on alternating colors, they are unable to attack each other.