Why do we need to pay land value taxes?

Because the land holder is excluding others from what was accessible to them had the land holder not been there. It is because that space has a value, which the land holder is enjoying only for himself, when other people can be enjoying that same natural resource and that same economic freedom. It is because the landholder is demanding from them to cede access to that portion of nature for his sake - and that portion of nature has a value, the market rent.