There's no real answer to the OP's questions until the terms "good" and "bad" aren't clarified.
While it's true that ethics are different between one society and another, there are more than a few traits which are shared by most people in the world.
Justifying someone's actions by saying that "they're not bad since evil and good are relative terms" is a naive and quite indecent statement.
We're genetically programmed to think that something is "good" or "bad". Every newborn has positive reactions to certain stimuli (things that taste sweet, human faces, mother's voice, well aligned mugs...) and negative reactions to other ones (things that taste bad, strangers' faces - around the 6th month of life -, scary mugs, and obviously painful things, etc.). This does not depend on culture, but at the same time it's something really immature and basic. Culture and education strengthens and gives more variety to an inborn formula of ethics. So, to keep this short, if the concepts of good and evil are relative, this doesn't mean that good and evil do not exist, but simply that a huge variety of good and evil exist at the same time.
To continue what I was saying, humans have some very basic inborn good/evil detection mechanism, but so far there aren't any known genes encoding an 'aggressive' / 'bad' character. Aggressive and more generally 'bad' actions in adults are being forged by education and society, so the correct answer would be the first one you proposed. This obviously does not justify anybody from his faults, since I'm pretty sure that people in most cases are not passive amoebas being forged by others but have their own intelligence and will to take actions and decisions.
If you're interested in some documentation on the matter, I'd suggest to read these: Bandura's Bobo doll experiment, Zimbardo's Stanford University experiment, Milgram's experiment on evil caused by authority.