Why do people enter into, and stay in, abusive relationships? Because abusers are good con artists.
Like a con artist, an abuser has something to gain from exploting others. Usually it's not money, although in some cases it may be. It's generally about power and control, and/or getting off on another person being emotionally or materially dependent upon them.
A good con artist can spot a "mark" for whatever their game is. Abusers are good at that too. They are able to find people who are needy and insecure, who have martyr complexes, who are too proud to admit they have a problem even when it's a very serious problem. Some people, for whatever reason, are just easy suckers for abusers.
When the abuser finds a mark, then the long con starts. They begin by playing nice, convincing the intended victim that they are a wonderful, trustworthy person. Once the victim is attached to them, or maybe addicted to them, they start subtly undermining her (or him), making the victim doubt their own intelligence, competence and judgment. They convince the victim to cut him or herself off from friends and family. The abuser presents their "wonderful" persona to the outside world so that no one will believe them capable of physically or emotionally abusing people in their family.
Look at this whole Chris Brown and Rihanna business. There are a lot of teenage girls out there who think Chris Brown is so nice and wonderful that Rihanna must have done something really bad and deserved getting beaten. Now that's a good con artist - one who doesn't even keep the abuse secret, but has a whole lot of people (including the victim) on his side, not seeing him for what he really is.
Masquerading and mind games are part of any abuser's tactics. Victims stay with abusers because by the time things start getting really bad, the abuser's got such a grip on their minds that he could convince the victim that down is up, day is night, and that they deserve to be treated like crap.