The fact is, stress is a prevalent and natural component of life. Even during simpler, more idyllic times, there was always a certain level of pressure that people had to deal with. The triggers that cause states of extreme duress differ from person to person, mainly because people have different levels of tolerance for it. Some may find a certain level of pressure to be absolutely intolerable, while others would be able to get through it relatively unscathed. Perspective and perception, in this particular case, appears to be the key factor in determining how much stress a person can handle. However, regardless of how one views the pressures that modern life piles up on a person, it still has to be dealt with somehow.
Complete avoidance of it is not the answer. Abandoning duty and ignoring things that cause stress would inevitably be a bad move. Stress, in smaller and more controlled amounts, can be used as a personal signal. It can act as a reminder that something needs to be done and certain situations need immediate attention, which can help someone in assessing his immediate and long-term priorities. So long as the cause of the problem is approached properly and the person doesn't let the problem blow itself out of proper context, then a bit of pressure is not necessarily a negative thing.
However, allowing the pressures of life to get to you is just as bad as simply ignoring them altogether. The human mind, while clearly a fine example of finely-tuned machinery, has limitations. Having too many things to do and not having enough time to do them can sometimes be seen as an example of poor time management, but for some people, having “too little time” means exactly that. Taking in too many tasks and attempting to multi-task beyond one's mental ability to coordinate can lead to rapid burn-out for some people, and irreparable insanity in others. It is people and situations like these that give stress the “entirely negative” reputation that it has, with people taking the whole thing entirely out of proportion.
In the end, stress is very similar to fear. Both are taken by modern society and culture in highly negative light, but both are components of the human psyche that are as integral to being human as love and happiness. Both can effectively cripple someone and prevent them from living, but only if the person allows that to happen. Both of the above need not be feared, so long as the person is capable of recognizing that moderate amounts can be used in a positive manner. Stress and fear, in and of themselves, are not positive, but like anger, can be used to point someone in the right direction.
