There were a variety of reasons. Some of them were around civil liberties. It was seen as a single database register of every single U.K. citizen, which is alien to U.K. culture, apart from during the Second World War when people had identity cards, which finished sometime soon after the war.
There were also technical issues with the design, partly reflected in the recent discussion about whether you build one big database into which you'd put all this quite sensitive data and then run the risk of it being breached. That would cause a bigger problem.