I don't know what to say. I thought the article structure made sense but I guess it didn't for you. What you call strawmen is what I commonly hear as arguments for mandates.
Thesis: Vaccine are good but mandates are bad
Background: advantages to vaccines, transmission data, current risks
Refute common arguments for mandatory vaccination 1) protect the vaccinated. 2) decrease transmission 3) hospital capacity 4) prior infection is inadequate
Review downsides to mandates: Harms and inconvenience to those who choose not to be vaccinated.
Conclusion
I think they key point they are arguing for is in the "bottom line" conclusion:
>If this were really about science, why would we not allow previous infection, which confers all the benefits of vaccination, if not more, the same rights? Does it not seem that mandates are having the opposite effect to what is desired? Instead of increasing vaccination rates are mandates instead hardening and alienating the unvaccinated further? If we are being honest with ourselves, are the mandates truly for the protection of the vaccinated, or do they exist to punish the unvaccinated?
I agree it would have been clearer if they stated their position as a declaration, opposed to a question, but it is right there