Because while there is no law or set of laws that can prevent every senseless act of violence completely, no piece of legislation that will prevent every tragedy, every act of evil, if there is even one thing we can do to reduce this violence, if there is even one life that can be saved, then we've got an obligation to try.
His first sentiment is accurate, thoughtful and, although regrettable, reflective of reality. It is true that those intent on harming or burgling are not all that interested in laws and the preferences of civilized societies, so in this way the President is merely acknowledging this truth.
The second sentiment regarding the bromide "if it saves one life, isn't it worth it" is depressing. Whenever a politician utters these words, you should be wary. Very wary. The real answer to this question – if we are to be honest – is likely, "No." The statement is often used to stir emotional and populist sentiments in order to forward some legislation that the speaker is favoring. It is used by many on both sides of the aisle and it is troubling no matter who says it. And I can assure you that most of those using it are brimming with good intention.
I am certain that reducing maximum speed limits to 35 mph would save lives – many more than one life and orders of magnitude more than any and all gun control schemes. Banning driving altogether would be even better – if vehicle fatalities were the only consideration. But when the costs are considered, the lives saved must be compared to the costs to society. Societies are constantly counting the costs and determining if the prescription is worse than the disease. Politicians are no more callous when they support higher speed limits that assure more fatlalities than they are when they oppose gun control measures that would do little or nothing to reduce gun violence and/or gun related deaths.
To the individual affected by gun violence, statistics and societal costs are meaningless. The murdered loved one isn't partially dead or statistically insignificant. So for the individual the platitude of saving just one life means everything. But a society must consider things more broadly and cannot make laws based on saving just one life. It is always a trade off between, say, freedom and reducing numbers killed.
Intoxicated driving provides a good example of the trade-offs. One might support stringent restrictions on blood alcohol levels as a way to reduce deaths on the roadways. But all alcohol related driving deaths cannot be prevented by this action alone, so one might think up other ways to 'save just one more life'. Roadside sobriety checkpoints may be a method by which one more life could be spared. However, roadside checkpoints have an element of presumed guilt such that the driver must disprove his guilt via a test administered by the roadside officer.
There are an infinite amount of issues for which some could argue from atop the 'if it saves one life' soapbox. Arguing against abortion, automobiles, energy production, ultraviolet rays, fast-food, drone strikes, cigarettes, and lawn darts would certainly save one or more life. Just as allowing the South to secede, swimming pool bans, peanut based food bans, never going outdoors, guarding embassies and schools resembling prisons would undoubtedly save lives.
And some acts aren’t as clear. And while one could argue that outlawing capital punishment would preserve the life of the convicted, there is ample evidence that ridding the world of some such evildoers would save far more lives in the long run if the evildoer is ever released and then commits more crimes. And weren't there more than a few that thought prohibition would save lives? Good intentions aside, prohibition likely cost many more lives than it saved.
Our society must grapple with whether gun bans or anything else that is promised to save 'one more life' is worth the abridgment of the Constitutional rights and individual liberty. The point is that societies count the cost, and like it or not, saving just one more life is not usually worth the societal cost. The answer to the question, "If it saved one life, wouldn't it be worth it?" is usually "No." And I suspect that would be the President's answer if met with a proposal to arm every citizen based on evidence that innocent lives are spared quite regularly by armed citizens rebuffing the unwanted advances of a criminal or rapist.