Resizing images always introduces distortions.
In some cases the distortions are acceptable. In other cases, the distortions are not acceptable, and you need to reconsider what you are doing.
If you resize this by 50% starting with the upper left:
Notice no 0's: the checkerboard pattern has been lost.
If you start from the upper right:
Notice no 1's, 2's, 3's, 4's.
Suppose you mean() each 2 x 2 discrete block and round(), starting from the upper left:
The first two 1's are round(2/4) -> 1, and the second two 1's are round(4/4) -> 1... clearly this is distorted relative to the original.
If you need to keep the "character" of being checker-board then since the output is only 2 x 4:
maybe?? Still obviously distorted compared to the original.
Resize to smaller must lose detail.