I think it's a combination of factors with regards to the "tax-resistant rich" as we'll call it.
Some of it is obviously purely greed (some people seem think they can never get enough, and think a dime of their own money is too much to chip in), it would be naive to deny that aspect. There are plenty of "Scrooge" types out there.
But I do think some of the tax resistance is rooted in more sincere concerns about the efficiency and stewardship with which that money gets spent, and fears that it could start becoming too easy to just start spending without planning. (The same reason lottery winners never seem to be as careful with their millions as a person who worked for it...and the same reason why kids start thinking a little more about their money when their parents make them get a job to earn vs. an allowance)
I think evidence of this is how some of even the left-leaning philanthropists choose to apply their money towards causes.
Bill Gates would be a perfect example. He's donated over $50 billion towards public health causes via private philanthropy (and committed a lot more towards that cause for when he passes away). Bill Gates certainly isn't an "anti-government guy" by any stretch. However, if he thought government was the best vehicle to achieve those aims, he'd just cut Billion-dollar checks to the US Treasury department and let them handle it. And I'm sure if you could ask him "Bill, would you rather pay more in taxes, or take the tax break, and be able to put your money toward the Bill Gates Foundation?"
Even going back to one of the biggest philanthropy guys of all time, Andrew Carnagie, when he funded the building of over 2,000 libraries in the US, he didn't merely hand the money over to the government. He played a reverse uno card, and made local governments and universities have to apply for grants from him, and he had to approve their architectural plans and they had to commit to an operational model he laid out in order for him to hand over the money.
So there definitely are rich guys (even generous rich guys who aren't anti-government) who just flat out feel that "those guys don't know how to manage and use money very well"