Brown sugar is just sugar that has been mixed with molasses. It’s essentially sugar mixed with sugar and there are all sorts of reasons to avoid that combination.
Low-Fat vs. Low-Sugar
The low-fat fad led to a rash of processed foods that were advertised as being low-fat, and therefore “healthy”. The only problem with that is artificially low-fat foods taste awful. So they added sugar to make their products more palatable. The result has been record high rates of obesity, diabetes, and heart disease. The list of medications the average American is prescribed continues to grow, and much of that can be avoided by simply eliminating (or at least limiting) sugar consumption.
The Dangers of Sugar
Among other things, sugar is known to depress immune function, increase inflammation, and even promote cancer (source). Different people have different reactions to sugar and some people can probably tolerate it in moderation, but due to sugar’s addictive nature, that moderation can be difficult to achieve.