What are the worst ways to die?
Different variations on running out of oxygen. In each case you have to deal with the panic of not being able to breathe. Have you ever had the wind knocked out of you? How sure were you that you were going to die right up until you didn't? Why would you induce that sensation on purpose? Except that's exactly what intense exercise does.
There is a point in exercise where your heart rate sky rockets, your lungs violently gasp for air, and laying on the ground doesn't stop the room from spinning. It hurts, it's terrifying, and anyone that claims to enjoy it is lying. What people enjoy is the high that settles in once your heart and lungs calm down. The trouble is you won't get to enjoy said high if you're having a panic attack, moving still hurts or feels extra hard, or you don't think you can drive safely. Feeling that you can't breathe or can't suck enough oxygen to catch your breath is sending you all the eminent signs of your impending doom. It's like a dress rehearsal for death, and your heart and lungs are giving the performance of a lifetime.
This is why the fear of being out of breath is rational. If you've never felt it before, or aren't used to feeling it, being out of breath is going dissuade you from doing what ever caused it in the first place. Combine it with the general anxiety of feeling like everyone is looking at you, and the belief that you look stupid or aren't good at what your're doing, and coming back the next day may require a miracle. Here's the thing though, the level of suckyness that feeling out of breath causes is the same for everyone. What changes is the amount of intensity it takes to reach the suckyness feeling.
So why would anyone voluntarily force themselves to be out of breath? Because the better conditioned your heart and lungs are for dealing with stress, the harder it is to reach the sucky feeling of being out of breath. The only thing worse then feeling out of breath during exercise, is feeling it OUTSIDE of exercise. You are at risk of finding yourself out of breath anytime you move with a purpose or for more than 5 minutes at a time if you aren't used to doing so. Being able to walk and talk and enjoy things all at the same time is not physically possible if the act of walking is making it hard to breathe. The good news is you don't necessarily need to be laying flat on your back and dry heaving after workouts in order to fix the issue.
There are sacrifices that must be made in order to achieve such an extremely high level of conditioning just like with getting a 6 pack, or deadlifting 500lbs. If your goals line up with something that intense, you will have to be willing to suffer the dry heaves that come with it. If you are not concerned with such an intense goal, or aren't really willing to deal with the sensation of being out of breath, that is ok. Just make sure to tailor your expectations and workouts realistically. Some level of elevated heart rate will be needed to improve your conditioning levels. Your body improves at things by being exposed to lesser versions of the real thing. These are small moments of stress that target a specific response. This is the same way you put on muscle, jump higher, or fight bears. There are things you can do however to prevent it from being full blown suckyness or panic inducing.
First: Spread the intensity of your exercise through out the week instead of in one big session. More frequent but not as close to death feeling workouts will give your heart and lungs the practice they need to improve without having to leave you dead each time.
Second: Rest between exercises. Push hard in each set and with each rep of your workout. Then make sure to let your heart rate recover before continuing.
Third: Trick your body. Cross train in your workouts. Mix high intensity, low intensity, heavy weight, light weight, and body weight into the same workout. The proper rest between exercises will make your body think you finished. The shock of doing a completely different style of exercise will jumpstart your system.
It is tempting to avoid being out of breath as much as possible. However! Avoiding the activities and work that cause you to be out of breath only increases the likelihood of it happening. Plus the acute levels of stress that exercise gives you act as an adrenaline dump for any other built up stress. Without a proper release for chronic stress your body will think you are sick and dying. You might not be afraid of this sensation, but unlike being out of breath from exercise, the consequences of chronic stress can actually kill you.