In addition to the reasons other have suggested, one reason that this is not done client side is that the PhotoDNA tech that is used for the fingerprinting is n

In addition to the reasons other have suggested, one reason that this is not done client side is that the PhotoDNA tech that is used for the fingerprinting is not something that Facebook can share or make available. It's primary use is in matching posted images with known databases of child porn images, so providing a mechanism for someone to reverse engineer the system and develop a means of bypassing it is not going to happen.