If you want to see why gun rights supporters are worried that their rights are under siege -- even by laws that don't actually prohibit the possession of guns for armed self-defense -- see San Francisco Police Code § 613.10:
In addition to all other requirements and conditions stated in this Article, each license [to sell firearms or ammunition] shall be subject to all of the following conditions, the breach of any of which shall be sufficient cause for revocation of the license by the Chief of Police: ...
(g) The licensee shall not sell, lease or otherwise transfer to any person any ammunition that:
(1) Serves no sporting purpose;
(2) Is designed to expand upon impact and utilize the jacket, shot or materials embedded within the jacket or shot to project or disperse barbs or other objects that are intended to increase the damage to a human body or other target (including, but not limited to, Winchester Black Talon, Speer Gold Dot, Federal Hydra-Shok, Hornady XTP, Eldorado Starfire, Hollow Point Ammunition and Remington Golden Sabre ammunition; or
(3) Is designed to fragment upon impact (including, but not limited to, Black Rhino bullets and Glaser Safety Slugs).
Many people don't want guns for "sporting" purposes. They want them to defend their and their family's lives. Why should the usability of ammunition for "sport" -- which presumably means hunting and perhaps competitive target-shooting (I don't include noncompetitive target-shooting, since all ammunition would serve that purpose) -- be relevant here?
Now I should acknowledge that the ordinance would still let people possess a good deal of defensive ammunition, since much of the ammunition that's used for hunting and competitive target-shooting is also useful for self-defense. A lawsuit challenging the ordinance -- brought by noted California gun lawyer Chuck Michel and by Don Kates, a lawyer who has also written many important articles on the Second Amendment -- argues (pp. 12-13) that the some of the specifically banned ammunition actually is especially useful for self-defense; but that's not my main point here.
Rather, my point is how the ordinance seems to deliberately marginalize defensive purposes for gun ownership. Sporting purposes are labeled legitimate, and other purposes, including defensive ones, are labeled illegitimate.
And of course if that is broadly done and broadly accepted -- once people buy into the notion that the legitimacy of gun use rests on its "sporting" applications -- further steps towards broader gun and ammunition bans become much easier. After all, the only thing that would be at stake in such bans would be "sport"; how can that measure up against the supposed crime-fighting (or even accident-fighting) benefits of gun control? Why not require that all guns and ammunition be stored at the range or at the hunting lodge, and never at home? Why not even ban the sport altogether, in the interests of saving lives?
So long as gun control proponents talk solely about "sporting purposes," and don't even acknowledge the legitimacy of defensive purposes, it's hard to take seriously the claims that law abiding citizens' rights to own guns in self-defense are safe, and that the only goal is supposedly "reasonable gun control" rather than broad gun bans.
By the way, such sporting purposes talk has been common among many supporters of restrictions on guns (e.g., Sarah Brady), and such provisions are present in various other statutes as well; I highlight the San Francisco ordinance since it categorically applies to all ammunition -- including that used for ordinary self-defense purposes -- and not just to specific subcategories of weapons or reecipients (see, e.g., 18 U.S.C. § 921(a)(4)(B)).