Don't be misled by the apparent mildness of this term. While the term 'being discouraged' is often used casually to describe a temporary state, it is also a deeply seated feeling of "what's the use, nothing I can do makes a difference..." At an extreme, it can be described as "learned helplessness".
Most abuse is aimed at discouraging the survivor so that she never exercises or explores options. More than just momentary cruelty, emotional abuse and verbal abuse is directed at lowering the survivor's self-esteem and 'power to do' things, on her behalf, and on the behalf of her children. Being discouraged can look like apathy, but rather than a lack of feeling, it comes from a paralyzing quantity of bad feelings. Some survivors stop taking care of their spirit or appearance when they have been discouraged, and ironically this too becomes a focus of abuse by the the primary aggressor.