But we can't blame those families. That's is their only way to get out of poverty.
That's true. The 'individual' is the weakest unit in any society, he cannot be blamed for trying to circumvent the realities imposed on him by decisions made by/for the collective. Having said that, I wouldn't extend the same logic to the muslims though because unlike the sample set for your case study (Indian poor), this sample set isn't exactly a product of economic engineering (global community of muslims). Their social engineering is steeped in theological endorsement of more children. The best way to verify this theory is to do an A/B testing and you will find that even if you swap all other economic indicators, nationality and economic models, there is a pattern of higher population growth amount muslims cutting across the spectrum and political or economic ideology of their nation.
There is a trend (not exception) of rich muslim families in capitalist western countries having more kids, poor muslim families having more kids, muslim families in socialist and communist countries having more kids, basically more kids regardless of other factors. One can't put the blame on poor economy or economic inequality in this case. It's purely theological. One could understand if it were merely culturally localized (like FGM) but it really is theological (like circumcision). More kids are considered good, primarily for theological reasons, the economic reasons are orthogonal and incidental and only sometimes economical.
Your theory applies to Hindus very well because when they are poor, they have more kids, but when there is upward social/economic mobility, the average number of kids is reduced. In a way this validates your theory, but same is not true for muslim families. Otherwise rich muslims wouldn't have had so many kids. For them, it's considered a gift from god, and they keep yearning for more gifts, regardless of their financial standing. The best testament to this is the man who is featured in the news himself (and many other Ghazis like him), when interviewed by news channels about their finances, they say "if I had more money, I could have even more kids, god willing". This directly contradicts your economic theory which equates financial upliftment with less kids. Here, the propensity to have more kids is not adversely affected by more income, on the contrary it is exacerbated.
Ideologically motivated people will continue to pursue an unsustainable game plan, you can't use any logical theory to rationalize their behavior. Ideology is inherently irrational. In short, jihadis will be jihadis.
