They don't have the added sugars or artificial sweeteners found in most bottled juices. Yes, fruit juice contains natural sugar, but that doesn't make it any healthier than the sugar in cola. In fact, the World Health Organization classifies sugar in juice with free sugars, just like sugar in soft drinks. Like fruit, fruit juice contains a number of vitamins and minerals, which is why some say it is “healthy”.
However, it also contains an enormous amount of sugar. These are nutrient superheroes and can obviously also be balanced in a juice, but exercise your taste buds as you get used to low-sugar juices. So a small amount of fruit juice seems OK, but too much sugar from all sources, including juice, is linked to poor health outcomes. Just as it's easy to make a great-tasting sweet juice with lots of fruit, it's even easier to make a really jaw-worthy juice by throwing lots of vegetables into the juicer.
Cold-pressed juices are said to be more nutritious than traditional commercial concentrated juices because they are less processed and are not pasteurized with heat.