6 ideas
A distribution is just if and only if it arises from just acquisition and just transfer — justice is historical, determined by how holdings came about, not by whether they match any pattern. This means you cannot evaluate fairness by looking at a snapshot of who has what; you must trace the actual chain of voluntary transactions and original acquisitions.
Any principle that maintains a fixed distributive pattern (equality, need, merit) will be continuously disrupted by people's voluntary choices, so enforcing it requires constant interference with free exchange. To preserve a pattern you must either forbid voluntary transactions or repeatedly confiscate and redistribute what people freely transfer.
Starting from any distribution you consider just, imagine a million fans each voluntarily pay a star athlete 25 cents to watch him play; he ends up vastly richer and the distribution is now unequal. Since each transfer was voluntary and the starting point was just, the unequal outcome must also be just — showing that 'liberty upsets patterns.'
Taxing the earnings from labor to fund redistribution is on a par with forced labor, because it seizes the product of hours a person worked and thereby gives others a partial property right in that person. Making someone work n hours for others' purposes is equivalent whether you take their time directly or take the wages those hours produced.
A minimal state can arise from anarchy without anyone violating rights, through a sequence in which individuals form protective associations, a dominant agency emerges, and it compensates independents it restrains from risky self-enforcement. The state thus appears as an unintended byproduct of self-interested rights-respecting actions, not a deliberate social contract.
Rather than designing one best society, treat utopia as a meta-framework that lets diverse communities form, each pursuing its own vision, with people free to join or exit. Because no single way of life suits everyone, the only viable utopia is one that permits experimentation among many communities rather than imposing a single ideal.