Brown is a true blue far left progressive. That movement assumes that almost all people are unable to correctly make decisions about their own lives; instead, an enlightened government bureaucracy must make those decisions for you. Why on Earth would people who believe you are unable to provide your own health care, day care, etc. trust you with a firearm? Only the State's agents, on the State's business, deserve to be armed. (And of course the bodyguards of the important people, that goes without saying.)
Besides, a key tenant of progressive "thought" is that the individual is worthless and interchangeable; only the group has value. If you get murdered by some gang banger or junkie, there are plenty of people to replace you so that government doesn't suffer. Besides, that gang banger or junkie is worth just as much as you, if not more - why should the State allow you to take his life to possibly save your own?