What does it mean that steel-man both sides?

Before resolving a contradiction make the strongest possible case for each side.

Example: Your team is deadlocked over whether to build a custom internal tool or adopt an off-the-shelf SaaS product. You favor building in-house. Before you argue your case, you force yourself to write the strongest possible argument for the SaaS option — not a caricature of it, but the version its most thoughtful advocate would make. You include the total cost of maintenance, the opportunity cost of engineering hours, the vendor's domain expertise you cannot replicate, and the speed advantage of shipping next week instead of next quarter. When you read it back, something shifts. You realize the SaaS case is stronger than you thought — not because you changed your mind, but because the argument you were planning to rebut was a weak version you had unconsciously constructed. Your original 'refutation' would have knocked down a straw man. Now you have to engage the real argument. And the real argument, it turns out, reveals a variable you had not considered: the maintenance burden of custom tooling compounds over years, while the SaaS cost remains flat. Your final recommendation is neither 'build' nor 'buy' — it is a hybrid approach that neither side would have reached without being forced to confront the strongest version of its opposition.

Try this: Identify a contradiction you are currently holding — two beliefs that genuinely conflict. Choose the side you find less compelling. Now spend 15 minutes writing the strongest possible case for that side. Follow Rapoport's protocol: express that position so clearly and completely that someone who actually holds it would say, 'Yes, that is exactly what I mean — I wish I had put it that way.' List every piece of evidence that supports it. Identify the conditions under which it is clearly correct. Make it as persuasive as you can. When you are done, re-read your original position. Notice what changed. The contradiction has not disappeared — but your understanding of what makes it a real contradiction, rather than a fight between a strong argument and a weak caricature, has sharpened.