There is a major cognitive barrier preventing most people from taking suicide seriously as a right, rather than classifying it as pathology. The barrier is that most people cannot imagine wanting to die.
Because people cannot conceive of wanting to die, they come up with all kinds of far-fetched explanations for suicide-related statistics. For example, Eva Schernhammer and Graham Colditz's review of twenty-five studies about doctors who committed suicide revealed that women doctors commit suicide at about twice the rate of women in the general population. In some studies, the women physicians' suicide rate approached parity with the rate of men in the general population (men commit suicide about four times as often as women, though women attempt suicide more often). Schernhammer proposed that a possible reason for the result could be gender bias in the medical profession. However, this theory does not explain the study's other result, which is that male doctors have a 41% increased risk of suicide over men in the general population. When we see more data - for instance, that British veterinarians have a suicide rate four times that of the general population, or that women chemists also commit suicide at an increased rate (as do male chemists, though not as much) - a more sensible answer presents itself. Physicians, like veterinarians, have access to comfortable, sure methods of committing suicide. A small minority of the populations wishes for death, but lacks appropriate means of achieving it - unless they happen to be doctors, vets, or chemists. (Incidentally, studies like these probably tell us approximately what the suicide rate would be if comfortable means were generally available - that is, still quite low.) It is ludicrous to suppose that people in these professions - but not, for instance, finance - are driven to suicide by gender bias or other career pressures. However, people naturally search for explanations like gender bias or job pressure, because they can't conceive of people in the general population wanting to die and not being able to do it.
In general, people find it hard to understand motivations of others that they do not share. Last night, for instance, four people shared a fish head casserole. Why did they eat this? If you have strong feeling against eating fish heads, your first thought is probably that poverty or desperate circumstances forced them to eat this dish. Or perhaps they ate it on a dare, or they were contestants on Fear Factor. But none of these is true. Three of my friends and I ordered the giant fish head - a Hunanese delicacy - and eagerly awaited it for thirty minutes while it steamed in a rich, garlicky poaching liquid with hot peppers. We had read a review of this dish and sought it out, and we ate it eagerly when it arrived. Neither coercion nor pathology is the proper explanation here - we did it because we wanted to.
A common reaction to an act motivated by a preference the observer finds mysterious is to attribute the act not to a preference, but to pathology, coercion, or some other motivation. In trying to understand the behavior, the observer thinks, "what would cause me to engage in that act? I'd have to be crazy, or someone would have to force me. Therefore this person must be crazy, or experiencing coercion." Perhaps this attempted-but-failed empathy and the confusion it generates could explain the hostile reaction to sexual practices the observer does not share, in a similar way to that posited by Nagel in his Personal Rights and Public Space.
Ultimately, of course, this principal explains why compassionate, kind people often have a hard time accepting suicide as a right. It is an empirical fact that most people do not want to die. They must find it very hard to imagine that others do want to die, that death is their genuine end. They use their own preferences as a model, and assume that the suicidal desire is a product of pathology (depression, a type of "crazy" conveniently defined to include almost anyone with suicidal thoughts) or coercion of some sort (temporary, remediable life problems, such as the "job pressures" mentioned above). The most important thing for the compassionate reader to realize is that some people genuinely want to die, and can't.