To most people who look closely, it's very obvious that when Warren Buffett proposes an inheritance tax that he is advocating for policies that helps his company. He isn't planning on giving very much of his money away in a manner than can be taxed by the inheritance tax and he runs a businesses that benefits from the tax. One way he benefits from an inheritence tax is through his life insurance companies, which benefit from the tax because their policies can be used to transfer wealth while avoiding some of these taxes. Buffett's company is also in the business of buying businesses, and when smaller businesses must be sold to pay the inheritance tax after the death of a founder the companies who systematically acquire these businesses from forced sellers end up profiting.
It turns out that a rising capital gains tax can have a similar effect on bringing bargain businesses to market. With a capital gains tax hike coming up, a lot of businesses owners are looking to sell, including some big names. In the US, corporations see no difference on capital gains and ordinary income so a capital gains tax hike won't impact his company negatively. Many non-profits are also exempt from the capital gains tax.
Most people running a business in the business of buying businesses would not benefit from a capital gains tax hike, regardless of the deals that became available to them from people looking to sell quickly. But because Warren Buffett is donating the majority of assets to charity, when he advocates for a higher capital gains tax he is also advocating for something that will help his business with little negative impact to himself or the causes that he is supporting.
Outside of lobbyists and politicians, most people truly believe that the policies they advocate will be the best option for society. But it's interesting when it turns out that a high profile advocate proposing a policy which seem to cause them harm (and thus gives the advocate's arguments slightly more credibility) actually benefits from the policy.