Earlier quoted context omitted.
Death is often called the great equalizer. By reducing/nullifying inheritance taxes you ensure wealth concentration will escape it, and aggravate the issue. We already live in a country (world, really) where more income is gained through owning capital than through working. However you look at it, it is really hard to justify.
I again fail to see how that is an argument that inheritence will increase wealth inequality. The headline is that wealth inequality will go up due to inheritence. Why would it go up over the alternative situation where nobody died and everyone just kept their money.
Take it as meaning that, were inheritance taxed, we could curb the progression of wealth inequality. But these taxes are getting relaxed, and so the issue worsens.
Also, with falling fertility rates, we may see more wealth getting concentrated in the hands of single childs. I am in such a case: I will inherit from both my parents, alone. (Although I am not really looking forward to this day). Here, wealth is getting concentrated in fewer hands through inheritance.