I think you're right.

It's not as if they personally manage every penny— and they tend to optimize for the highest return as a default.

Seems like he's saying the default should change. Makes sense to me.

Then they should say what they mean instead of being, as I mentioned, all passive aggressive about it.

I don't think they are - I think it's just a misunderstanding of phrasing maybe?

I interpret "I should have paid more" as I should be compelled to pay more, not "I wish I could pay more". The distinction being they'd rather not pay additional tax, but they probably should have to. I think the language is just somewhat ambiguous (specifically the word 'should').

If he thinks that the government can better allocate the collective amount of additional tax it could obtain from people in similar tax situations, why wouldn't he think the same about just his portion?

Either he has a much higher opinion of his personal judgement in allocating his money (which is likely) than other people who he also thinks should be paying more tax or he should turn over the BMGF to the government.

I expect that it's not so much a higher opinion of his personal judgement as a higher opinion of his values and priorities. Obviously he feels their foundation is spending money on the most important things it can be; however I expect he also feels that the government will, on average, spend it on more important things than it would be used for by most people with similar levels of wealth.

So pretty much the same way most people think that their driving skills are well above average.

To be fair, Bill Gates probably is above average in a lot of ways.

Because his portion, however huge it is, is a rounding error compared to the US government's budget. But everyone in his class put together, if you make them all pay more, then it becomes a significant amount of money.

>why wouldn't he think the same about just his portion?

well Bill Gates personally does which is why he is giving almost all of his wealth away. (The giving pledge exists for this reason, and I would assume that most billionaires who agree to higher taxation also are significant personal givers).

This criticism fails on two fronts. People who are in favour of increased tax redistribution generally also support voluntary giving. (Most of the effective altruist people I think would fall into this group), and even if they didn't it would be nothing more than a cheap personal attack, because one can hold positions in favour of tax redistribution and against charity at the same time.