It'd be interesting to point out to her the ratio of on-duty LEO's to the population of your city/county - I don't know what the numbers are for you, but where I am (San Jose, CA) there are typically between 90 and 120 patrol officers responding to calls for a city of a million people.
Our local PD classes calls into one of four categories, from 1 (present or imminent danger to life; major damage to or loss of property), 2 (injuries or suspected injuries; suspect still present) to 4 (non-violent crime with no apparent danger to life/property).
The most recent data I can find is from July 2004 through September 2006. (The staffing levels of our local PD have declined since then.)
The average response time to a priority 1 call was 7.23 minutes; the average response time to a priority 2 call was 12.73 minutes. Our PD defines "response time" as the elapsed time from the call-taker's first keystroke into the dispatch system until the arrival of the first officer on the scene.
A lot of things can happen in 7.23 minutes - and that's the average, so half of the time, it took longer than that for the first officer to show up.
(And half of the time, it took less time. I'm not saying this to bash the PD, but to consider what the average or worst-case scenario might look like from a citizen's point of view.)
Law enforcement has (generally speaking) no legal duty to protect you. How could they, if there are 100 patrol officers on duty and 1,000,000 citizens?
Practically speaking, it may take 10-15 minutes before you get a response to a call to 911, even if the event you're reporting is very serious. (In fact, if it sounds too horrible, the first person on scene will probably wait for backup, not go charging in like the Lone Ranger.)
The bottom line is that you're on your own - potentially for as long as 15 minutes, maybe even worse. If something awful happens, you must respond to it with whatever you've got with you or on you at that moment - e.g., what's in your pockets or your purse or your backpack/briefcase - and whatever you can find or improvise from your surroundings.
If the problem you're faced with is an attack or a threat from a violent person, it'd be much better to have a good weapon (like a firearm) available to you. Yes, a LEO will be along, eventually, and they will be armed - but it may take so long that by the time they arrive, whatever bad thing the attacker had in mind for you has already occurred, whether that's robbery or rape or murder.
This will never be very different, because it's very expensive to keep people trained and equipped and paid to act as LEO's, so we're never going to have a great LEO:citizen ratio, especially if we don't want to see our tax rates go through the roof.
