This is a questionable premise. After all, it is globalization that has allowed for the rise of China, which was very much a "developing country" a decade or two ago and is now an economic power. Globalization really has helped many developing nations catch up to the more developed nations. Globalization does seem to contribute to increasing inequality within nations, but it does not seem to contribute as much to increasing inequality between nations.
However, if you have to argue that it does, you can argue that globalization allows developed countries to treat developing countries like colonies. The developed countries, you can argue, let the poorer countries do the low-paid, low-skilled jobs that do not create much wealth. The developed countries can also buy raw materials from the poorer countries without really helping those countries to develop. You can say that globalization lets the rich countries exploit the poor ones by buying cheap things from the poor countries without really helping those countries progress to the point where they can compete against the developed countries in producing things that are more profitable.