It seems to fundamentally come down to people not wanting the government to have records that connect them to their firearms. I live in a state that's gotten somewhat nutty lately; we already did not require any firearms registration for private-party sales, so not only are background checks less effective as second-hand purchase avoids them and registration entirely, but we've also taken away a need for a concealed carry permit, so now anyone can carry a concealed firearm without any need to undergo training or to demonstrate proficiency (which were previous requirements). The need to obtain permits in the past was one tool available to the citizenry and the police to determine who, most likely, was carrying for personal protection (ie, those with permits) versus those who were carrying with bad intent (ie, those who didn't get permits and were carrying illegally).
I didn't think that the burden to obtain a CCW permit was especially high. Demonstrate that you can shoot and actually hit the intended target, and review situations when it is and when it is not appropriate to introduce a firearm. That was basically it. Unfortunately, there were those who felt that this was too much of a burden and they got the law changed.