There are a number of flawed assumptions here. The first one is that population growth is naturally unbounded, but that idea has been outdated for a long time. Population growth follows a logistic growth curve.

Another bad assumption you're making is that the West's population is growing rapidly, but it's not. In fact, populations in Western countries are barely growing, and often are only growing due to immigration, or due to higher birth rates among immigrant populations.

Finally, yet another bad assumption you're making is that we should limit population growth through draconian measures like… well murdering people, or allowing them to die unnecessarily. In fact, the best way to limit population growth is through education, better access to healthcare, and economic development. As people become more educated and financially successful, they naturally delay childbirth and have fewer children as a result. When people have access to health services like education, birth control and abortions, they can better make decisions about children.

You can google “overpopulation myth” or simply “overpopulation” to verify what I've written here.