I appreciate Bill Gate's charity work but I understand that it also doesn't benefit me personally - It probably costs me as well. Lifting people out of poverty means that they will be able to get an education to compete against me in the job marketplace in the future and will lower my wage. I can cope with that on a moral basis, but I'm pretty sure that Bill Gate's donations cost me more (in terms of how it affects my humble net worth) than it costs Bill Gates himself (in terms of how it affects his net worth).
With the technology we have now the world does in fact have plenty of resources to have basic needs satisfied for everyone (e.g., we throw away many times more food than what it would take to fix hunger). There is no actual need to compete. Such a world is safer for everyone, including the rich, and Bill Gates is one of many working long term towards that goal.
See lifting the poor as a rather cheap insurance against political instability.
We are always one major war or one generation away from having the entire system toppled, and the very meaning of "property rights" that make the rich rich overturned. Civilizations are not forever, whatever the people currently at the top may hope for.
Intentionally keeping the poor poor, and keep concentrating wealth, is not a recipe for stability.
I agree that it's very complex though and we can't really measure how much Bill Gates' philanthropy may have contributed towards this trend.
I just wanted to point out that good things tend to have negative unintended side effects. For every deal, there is always a winner and a loser.