There is a distinction to be made between an obligation not to cause suffering and an obligation to prevent suffering. The former is almost universally accepted; the latter, to put it simply, is not. People agree that murder is seriously wrong, and insults are at least somewhat wrong. On the other hand, most feel that, while protecting others’ lives and reputations is a nice thing to do, it is not morally obligatory. Is this latter perspective defensible?
In order to determine if there is a moral obligation to prevent suffering, let us examine whether there is a legitimate difference between causing suffering and failing to prevent suffering. If there is no difference then there must exist a moral obligation to prevent suffering.
The answer to the question at hand depends on why there is a moral obligation not to make others suffer. There are two primary motivators of moral obligation (and, more generally, of morality itself): consequentialism and deontology.
Deontology, or rule-based ethics, puts forth certain moral rules that must be followed unconditionally. There are some rule-based systems in which there is an obligation not to cause suffering, but no obligation to prevent suffering. The classic case of deontological ethics is Kantian deontology, in which rational agents must be treated as ends in themselves and never merely as means to an end. To inflict suffering on a person is to treat him as a means to an end, which is clearly immoral under Kantian ethics. There is no prohibition, however, against failing to prevent suffering. Other deontological schools of ethics often come to the same conclusion.
Under a consequentialist system, there is no fundamental reason to distinguish between action and inaction. Whether one is causing suffering or failing to prevent it, the outcome is the same: suffering occurs, and that suffering could have been prevented. An actor is morally obligated to prevent suffering to precisely the same degree that she is obligated not to cause suffering.
Given that consequentialism is the only sensible option, let us adopt the consequentialist viewpoint.
The only reason to distinguish between preventing and failing to cause suffering is if there is some benefit in creating such a distinction. There is indeed a benefit in making the distinction, but it is related to the enforcement of morality rather than morality itself. People almost always fail to cause suffering in others, so it makes sense to make it illegal since infractions will be relatively easy to deal with. For example, murder is rare so it is possible to enforce laws against it; but if it were far more common then the laws against it would be unenforceable, and would be repealed. Of course, even if murder were much more common, it would still be morally wrong.
There are many cases in which people could prevent suffering but do not, so laws requiring people to prevent suffering would be unenforceable. In fact, even where people are perfectly able to prevent suffering, they almost always do not: thanks to increasing globalization, the most prosperous people can easily reach out to the people who are suffering the most, and yet they do so only occasionally. However, just as murder would not be ethical even if everyone did it, one cannot justify failing to prevent suffering by the fact that it is so common.
Under a deontological system, it is possible that there is a difference between preventing and failing to cause suffering. But according to consequentialism, there is no such difference.