URLS redirections after website redesigning

So, we are about 1-2 weeks away from launching our new website after a redesign. I am a communications specialist and I have been working with a contractual backend dev (and a marketing firm for the ux and frontend part of the project, but their part is done).

We are at the step of getting the technical stuff ready to go live, but I am in some sort of argument with the backend dev. He is...old school.

I asked him to do a 301 redirections to some key pages of our website in terms of trafic and importance for our organization. The goal is to redirect each of these pages from our old website to pages on our new website that have the same content or the closest content possible. On our new website, some of the urls of content will be different. I offered to send him a short migration plan.

The dev says its not necessary because we have a small website and google will automatically re-index all the pages that changed urls anyway.

However, I have made my research and all the ressources about content migration and new website say the same as I do.

Am I wrong here? Am I planning to do more work than whats necessary?

Thanks for your help! The dev makes me dpubt now...