According to their statement, Bethesda had been in talks with Sony for months over mod support, but Sony would not allow mods to work how the company felt they should: enabling players to do whatever they want in Fallout 4 and Skyrim.
Bethesda expressed its great disappointment with the situation, and hopes to find another way to allow players to use mods on the system. However, with no support from Sony, it seems this feature will remain an Xbox exclusive.
If there are any updates, Bethesda will keep fans informed on its official website.