In writing (or reading), imagine how boring a character would be if they were just angry or only sad. A purely evil or good character is not only unrealistic, but also quite dull. Yet, think of how interesting a murderer would be if he/she also always visited his grandmother with flowers.
Personalities are tricky things, but one thing I noticed is that they are not necessarily generalities. For example, just because someone is a bully to one person does not mean that they are bullies to others. Just because a person is angry in one situation, it does not mean that they are angry in others – no matter how similar. What can influence behavior and emotion can be quite subtle.
It is a mistake to describe someone in blanket terms – e.g., he is a very angry person, she is very smart, etc. Rather, one should recognize that this is just how she/he had been observed that individual (you). The act of observing perhaps even influences behavior and how a personality manifests.
I personally have very complex relationships in real life with people who I know who are kind and generous, just not necessarily to me (e.g., ex-girlfriends come to mind, but certainly not only them). In a way, that is a tragedy – that there is perhaps something about me that prevents this person from expressing their better angels. I also know that I am certainly not alone in experiencing nor in expressing this. I find that I am almost always guilty of the things I observe in others.
Nevertheless, this is very helpful in writing. A person who is angry towards one character can be kind to another, and that may not necessarily be contradictory. Rather, that makes the character complex, and in writing, this tragedy can be put to use by creating engaging and frustrating and sympathetic and interesting characters. It is something I am using now in my novel, and I find myself becoming more immersed in the story as a result.