Fasting and abstaining are the foundation of the mortification that every Catholic must have to save his soul.
The only question is, how much and how often.
We must keep our love of food (=love of pleasure) in check, or it WILL get out of control -- it will control you. On a practical level, when it comes to actually achieving this, some people have to work harder at it than others.
No one should completely excuse themselves from mortification -- even a sick person in a hospital bed can forego a piece of candy, eat deliberately slower, sprinkle something harmless that makes the food taste less pleasant (or forego seasonings), etc.
The taste of food has nothing to do with being healthy -- in fact, many healthy foods aren't as tasty as McDonald's french fries (which a lot of people seem to like -- I avoid them myself), and many "tasty" foods are positively horrible for you. So much for that excuse.
As you can see, being sickly or of poor health shouldn't excuse one from denying himself.
The old rules for fasting and abstinence provided most Catholics a good minimum to maintain a decent level of mortification. The post-Vatican II Church did away with virtually all fasting and abstinence. This does not meet the needs of a fallen human nature struggling against original sin. What must we do?
We have to choose some mortifications -- why not start with the Church's old pre-Vatican II rules? Giving up meat on Friday, etc. won't kill a person.
With regard to the specifics, you need to tailor your penances to what your body can handle. For one thing, many foods are so denatured these days that you "crash" a couple hours after eating them. I've learned what those are (potato chips, virtually all cold cereal -- even the healthy ones, sugary foods, etc.) and avoid them completely on fast days. The old Church fasting rules even stated that you should eat enough food to "maintain your strength" -- not feel like you can jump over a fence, but I would interpret that as "don't feel weak and shaky -- don't incapacitate yourself". Drinking fluids between meals is allowed -- if you need to, you might even resort to drinking milk. Better that than to skip fasting altogether.
Many saints have spoken about excessive fasting. Nevertheless, I don't think most people have to worry about that today! Quite the contrary.
I know the Church used to have dispensations for those doing hard manual labor, etc.
In short, the Church just wanted us to control our sensual appetites and put to death the Old Man spoken of by St. Paul -- not kill ourselves or render ourselves unfit to do our duties.