Because the storm break could be a relatively simple dike, a thin structure jutting out, instead of a massive artificial island.
There will be hundreds of trucks driving through Copenhagen every single day for decades, to dump the necessary dirt to construct the island. That is going to cause massive noise and disturbance problems for people living in the city, all for a prestige project that has been hastily jammed through, including a runaround on environmental regulations.
The end result will be even more unaffordable luxury apartments, which will be bought by rich investors, creating yet another dead area devoid of local culture and life, just like Ørestad and Nordhavn, where a huge number of expensive apartments sit completely empty, bought only as investment objects.
A much better alternative would be to construct a simpler storm break, and then expand Copenhagen westwards, increasing density in the suburbs and outlying areas, by predominantly building affordable apartments and ensuring good public transit coverage, to combat the current situation of students and working class people being pushed out of the city by ever-increasing housing prices.