1. Sport is for professionals. This idea applies only in the case of performance sports. The native qualities required for professional sportsmen (speed, skills, specific height, etc.) can only be developed, they can't be formed by training. As long as the aim of a regular person is not performance, almost all sports can be practiced for keeping the body in a good shape. It's all about dosing the training you chose, so that the benefits are bigger than wear and tear. Even the sports considered tough can be practiced in a 'soft' way (tae-bo, mini-triathlon, jogging, etc.).
2. Training is tiring. This idea is true as long as it refers to consuming all your energy (muscular and hepatic glycogen), but it doesn't mean that training gets you into that state of exhaustion which would slow down the process of recovery of the body. Even in performance sports, the purpose is to have rather effective than exhausting training, so that the body can get the stimulation necessary to qualitative progress from one training to the next.
Even more than in other sports, in fitness the sportsman is spared overexerting. However, the training must not become ineffective. People can come to the gym tired after a work day and leave relaxed (physically and psychologically) and not more tired. This is extremely useful for people with sedentary jobs, but also for those who make physical effort at work. They could use the training by choosing a type of effort meant to compensate the one involved in their job.
3. Training takes too long. Again, this idea is true if applied to performance, which can only be obtained by working a lot. But also in this case short and very intense training or training for relaxation and recovery are often performed. In fitness, you can get to 20-minute training, working only super-series of fast exercises, which could involve, directly or indirectly, all the muscles. Anyway, regular training shouldn't take longer than an hour and a half. Otherwise, the body will get into the catabolic faze, when the cortisone secretions 'cannibalize' the muscles.
4. Any type of exercise is good for solving your problems. What's true in this refers to some particular cases like excess of adipose tissue. This tissue can be 'melted' by any kind of aerobic exercise (running, cycling, swimming) if this is continued long enough. Even in these cases it was clear that some exercises are more effective than others. There are situations when only a combination of exercises with a certain amount of each, can provide you with the results you expect. More than that, repeating the same exercise all the time can have as a consequence not only losing balance in the antagonist muscles and in the joints involved in training, but also stopping progress or even regressing.
5. You're older? No more exercises! This is true only if we refer to extremely demanding efforts (really heavy weights, fast running, jumping, etc.). There are lots of exercises adapted to different ages. Their purpose is to keep and improve health and also to improve physical shape. The development of movement parameters for older people refers especially to muscular and cardio-vascular resistance as well as mobility of the joints. Because the final purpose of training is not preparing for a competition, the exercises can be organized gradually according to their difficulty, eliminating the risk of accidents. Because it's based on perseverance, fitness can be adapted without problems for older people and even for people suffering from different affections specific to old age.