Why do some women want to date married men and break up marriages?  Do you think they just want what they can't or don't have?

Do you honestly think the men that stray are so innocent? Many of them are either not even bothering to say that they are married until they've got the other woman hooked or they tell them that their marriage is falling apart, they never have s*x anymore, he's only staying for the kids. Sometimes it's just a matter of working long hours together and that he truly has grown apart from his wife. But to blame "the other woman" for a man that is clearly not committed is a cop out and misdirected anger.  The other woman is not the one in the committed relationship. You have no idea what he's telling her, how much he's flirting with her. She would not likely be pursuing if she wasn't getting feedback.

Look at so many shows that show relationships as a battle for supremacy.  A few women continue this pre adolescent behaviour into adulthood.  They WANT to break up marriages to prove that they have a higher value than the wife.  Not many but some are like this.

There can be lots of reasons. For some women, they don't care that the man is married and they just want him any way they can have him. Others truly love the man and believe that he will leave his wife for her. For some, it's because they think they're getting all the best parts of the relationship (like sex, gifts, attention) without the downside. There are women who enjoy the excitement and wrongness of dating a married man. And yes, some people just want what they believe "belongs" to someone else. 

I agree with you and think this is one of the reasons some women date married men.  It's sad and unfortunate but it's reality.

Another reason some women do this is because they see a man who is stable and likely a good family man.

Married men tend to be attractive to other women. Some married men take advantage of that. The other women don’t attempt to break up marriages; they fall in love with married men. 

Dating is just dating. The married men shouldn’t date other women, regardless of what those other women might want.

They see what they want and don't care about the consequences.