No, they're widespread opinions. Laws usually come about because people think they're good ideas; why would legislators work to enact laws that everyone except for me was opposed to?
People who inherit wealth didn't work for it, and didn't earn it. Some heirs might be in a desperate way, and it isn't bad to help them get on their feet. Others might inherit items of significant sentimental value but which aren't fabulously valuable and that's not so bad either.
But there is no gain to society for a select few to become particularly wealthy in an undeserving manner, such as by inheritance. In fact, it's dangerous, because wealth tends to provide power, and now you've got people who have no rightful claim to great wealth also possessing great power and likely using it for ill. Certainly that's the usual way things go, and we should adopt rules for the usual case, and not for rare exceptions.
And it's not odd to see wealthy people perfectly in favor of estate taxes. Here's something from Andrew Carnegie's book:
The growing disposition to tax more and more heavily large estates left at death is a cheering indication of the growth of a salutary change in public opinion. ... Of all forms of taxation this seems the wisest. Men who continue hoarding great sums all their lives, the proper use of which for public ends would work good to the community from which it chiefly came, should be made to feel that the community, in the form of the State, cannot thus be deprived of its proper share. By taxing estates heavily at death the State marks its condemnation of the selfish millionaire's unworthy life.
As for progressive income taxes, ability to pay is the best way to go. It works. People are okay with it.
An absolute flat tax is pointless unless the amount you need to raise is very very low: taxing everyone, say, $100/year will result in some people easily being able to afford it, others barely able to afford it, and quite a few simply unable to afford it. Saying that it's fair that each person should pay the same quantity doesn't help them get it in order to pay it. You will wind up with a lot of people not paying their taxes, requiring either piling unjust punishment on top of their existing poverty, probably at the expense of the state, thus requiring even more taxes to proceed, or a de facto progressive taxation system in which people who are unable to pay are allowed to slide.
A proportional flat tax similarly fails. Below a certain amount of income, people simply cannot afford to pay, even if the tax were merely 1%. Unable to get blood from a stone, you must again either punish poor people for being poor, which is the sort of thing that justifies having your head cut off by an angry mob with a guillotine, or you wind up adopting a progressive taxation scheme and merely being a hypocrite who is saddled with a stupid tax system.
Some flat tax proposals suggest including various measures to avoid this, e.g. only kicking in above a certain level of income. This means that they're not actually flat taxes, they're progressive taxes which have two brackets, and are thus simply poorly designed. An ideal progressive tax, OTOH, would probably just be a mathematical function, with the tax rates varying smoothly as income varied, but for the sake of simplicity, we tend to have a number of brackets.
As a closing word of advice, you may do well to google things quickly on your own, rather than demanding answers to cover for your own ignorance or as a crappy rhetorical device.