If you look at the Russian women who are looking for husbands abroad, so many of them have advanced degrees and professional jobs like lawyers, economists, accountants, medical doctors or engineers - they are not poor Russian girls looking to get out of poverty!
And this is why the question "Why Russian women want to leave Russia" is ultimately wrong; Russian women want to find a good man for marriage - this is the goal, not leaving Russia or immigration.
Leaving Russia (or her other home country, Ukraine, Moldova, Kazakhstan or any other country of the former Soviet Union), leaving Russia will be very hard for her, losing her family and friends at once and moving into unknown country to start her life all over, but the cultural standard for a woman to have family (marriage and kids) as her highest priority is so strong, some women are brave enough to look into unknown and start looking for a partner abroad.
In other words, good men in Russia are rare - by a good man I mean a man who doesn't drink, doesn't sleep around, doesn't abuse his wife and is able to hold a stable job and provide for the family.
Russians have mobile phones, international fast food chains and Mc Donald's, Internet, IPAD's and latest cars (Moscow has the highest number of Mercedes and BMW's of all world's cities, including Germany - and Moscow has more dollar billionaires than New York! Yes, Russians live mostly in small apartments as compared to most western countries where people live in small houses in suburbia, but look at Manhattan in NY, this is very similar. So, living conditions whilst yes, there is some difference, it's not like Uganda or Vietnam vs. I can tell you living conditions and better life were NOT the reasons why I started to look for a husband abroad.
I didn't want to "leave Russia"; this wasn't the goal.