Whenever there is a finite number of resources it becomes an auction type of zero sum game. So, if someone else has the asset then I do not get it.

For example, I would love to own some camping/hunting property. Let's say that acreage comes available which both me and a billionaire really like. The fact that they have much more wealth than I do means that I don't get the property. The larger the wealth gap gets, the more assets are held by a few that otherwise would have been spread among the many. This obviously becomes an issue in politics as support from a rich man becomes more important.

This applies to not just assets. It also includes access to experiences. For example, I would love to own lower bowl season tickets to the Jazz. There is a limited number of the available, so it becomes an auction and I will not win because others have more wealth. Also applies to access to expertise. For example, best doctors, lawyers, chef, etc.

Overall, don't fool yourself that wealth inequality doesn't hurt anyone. In fact, the only group it helps is the top tier.