So what is so bad about being a Divergent?

The reason for the hatred and feeling of fear towards divergent is because they cannot be controlled. The world that they show follows the rules and strict principals. Divergent people do not necessarily follow these rules and it is speculated that sooner or later they will break out of the norms and defy the principles and rules of the world and will be a danger for themselves and for everyone else since they will disrupt the smooth flow of life around them. Apart from that, I guess another reason would be that they will question the system and demand justification for the housing system as to why is there a need of dividing everyone based on their test results. The authority would not allow that so they fear them and hate them

This question is difficult to explain without including spoilers from the other books/ planned films, but basically know that it isn't only the fact that they aren't controllable that makes divergents hated. It has a lot to do with jealousy, since the divergent are actually different genetically than those who fit specifically into a faction. the leader of Erudite knows something about the origins of the society (did you ever consider how the world got to the state in which they are living? it's explained later) that the rest don't know. I understand the confusion, since with any book/film adaption there is a crunch to transform relevant information into a more condensed and passively absorbed form of media.

Divergents don't fit into a category. The structure of society is based on everyone fitting into a category.

This is a popular, powerful theme in young adult fiction, since many young adults are unsure and nervous about where they "fit" in the world. Divergents represent those young adults that are afraid they don't fit into one of the preexisting categories in society - Erudites, Dauntless, Abnegation in the movie/book ... or in the reader's/viewer's world, Investment Banker, Store Manager, Dental Assistant, Data Analyst, Cook, Graphic Designer, and so on.

(In the movie/book, Factionless people don't fit into a preexisting category either, but many of them were rejected from the categories they fit into, like Dauntless.)

Here's a more philosophical take on the movie/book premise.

In modern society, we have a tendency to label things and put them into specific categories. When we label people, we tend to call these stereotypes. These allow us to make quick judgements while knowing very few facts. In some instances these categories are helpful, but in many they are also hurtful.

The problem with trying to categorize everything though, is that not everything is easily categorized. For instance, you could categorize people as either introverted or extroverted. However, there's no clear delineation between the two, because it's more of a spectrum than a clear either/or. For a lot of categorizations that are either/or, there are a lot of edge cases that blur the lines between the two.

The ultimate fear of the divergent members of society are that they don't fit into the accepted categories. They are an unmeasurable unknown. This specifically bugs the Erudites because to them, everything MUST be categorized and everything MUST fit into their perfect world, but these people don't, and never will. As such, they must be eliminated because they break everything.

The reason that it was bad in divergent was because that they had the factions. People like Jenean believed that divergent would ruin the faction system because they fit into all the factions. For jenean, that was a problem because she wanted everyone to have their own job and personality. She said that the faction system was to 'keep the peace' that why she hated divergents. Apparently they would 'break the peace'.

SPOILER ALERT FOR INSURGENT

Obviously she was wrong as in insurgent Divergent were the solution of the faction system as they opened the mysterious box.