Why do they believe you would go broke pursuing code? Have you tried pointing them to some articles or statistics on the high levels of salaries software engineers make? I'm sure you know they make more than many professions, and the demand is ever rising. Seems like this should be an easy debate to win :)
I don't think you understand how different things are in the developing world. It took me 5 years and an international flight for them to the US just to make my parents understand the difference between pursuing a degree in CS and pursuing a degree in typing.
It's not that they are ignorant, it's a lack of exposure and also just tough circumstances that may make it seem unrealistic.
It's not necessarily easy to explain this concept to people living here in the US, unless they know someone who's made it work. The idea that a non-Doctor/Lawyer/Architect can make a decent life for themselves and provide for a family is only gradually catching on.