I'm pretty sure it's that she pays a higher rate than he does. He pays more taxes every year than she'll earn in her lifetime.

Exactly, which he says is stupid. That's why Buffett and Gates have been pushing so hard to get other billionaires to pledge to donate as much as them. Larry Ellison is one of the more recent tech execs to take the pledge.

Last I read Larry makes 1.6 BILLION US DOLLARS a year. I don't think you can ever spend that much money.

For what it's worth, Larry Ellison also personally started and funds the Ellison Medical Foundation, which distributes on the order of 100 million dollars (cite: wikipedia: Larry Ellison) per year to leading academic biologists for research into the diseases of the elderly and how to stop them. Grant recipients are selected by a panel of scientists.

Larry seems to take this as a challenge.

Larry's taste includes fighter jets...

pretty easy to spend that buying a few private jets and yachts. 1.6 billion ain't what it used to be.

Not more in taxes but more as a percentage of total earnings. The tax bracket was higher for the secretary whereas for Buffett it was around 18% (iirc).

The capital gains/dividend tax breaks basically benefit the rich. Cap gains/dividend taxes should be on a marginal basis just like ordinary income.

The idea behind lower cap gains/dividend taxes is to incentivize investment (over consumption or savings). I'm no expert with the economics literature here, but I would worry about making changes that make it harder for businesses to access capital.

You don't have to throw the dice and hope, you can go look at most of the other 1st world countries that don't have this and how they're doing. Hint: just fine.

So why isn't he campaigning for lower taxes for her instead of higher taxes for others?

Because you will need to raise taxes for them to pay for lower taxes for her

Not necessarily, you can reduce government spending.