Divorce question ?

Couples usually go through some kind mediation to figure out what to do with a family home. Sometimes they're mature enough to not want to disrupt their kids' lives more than necessary by having them move (and go to new schools). So whomever they decide should have the weekday custody will usually remain in the home even though they both still own it. I've also heard of people with shared custody who move themselves back and forth into and out of the family home so their kids can have both parents in the house they're used to just on different days of the week. Almost all of the time when there aren't minor children involved couples just sell the house and split the proceeds. 

When you say it's "usually" the other way around, where are you getting this?  Nobody really has any idea, other than what they've observed in their own very tiny circle.

There are lots of reasons men get the home.  Sometimes it was their parents' home and they inherited it.  Sometimes men get primary custody.  Sometimes it's the wife who cheats and/or leaves the marriage.  Sometimes the wife wants to move to her home state and the court decides the kids are better off staying in THEIR home state.  Tons and tons of reasons!

keeping the house is often not a real prize as much as a trophy in a pissing war where everyone looses 

the simple reason could be she cannot afford the payments or upkeep 

do not let that be a trap you fall in, my sister in law got the house then lost it to the bank ,,,, she was being mean and she slapped her self in the face with it 

Perhaps because the wife can't afford the house/mortgage payments.

It depends upon the laws in their state.  Most states are community property states.  This means the house is sold and the proceeds are split, unless one party buys out the other party's half.  When my sister got divorced, she owned half of her husband's business because she provided the start-up capital and supported him for the several years it took him to make a profit.  She traded her half of the business for his half of the house.  I have a friend who wanted to keep his house because it was close to his office and allowed him to walk to work.  He paid his wife half of the assessed value of the house in order to keep it.   It depends upon their motivation.  If kids are involved, it's not uncommon for the custodial parent to stay in the house to provide continuity for the kids - they don't have to change schools or make new friends.  Others may not be willing to stay in a place with bad memories and are eager to move.