what data would you have used to back up your claim
I'd ask that question of your manager. If they can provide data that shows a statistically significant number of your customers read your site while resizing their browser at the same time and are frustrated to the point of losing them, maybe your web site is a statistical anomaly and just isn't suited for responsive layouts unlike a vast majority of web sites out there.
OK, maybe don't say that. Not all managers may appreciate that approach. :)
This is a hole we in UX sometimes dig ourselves into. We love using data to back up decisions (as we should) but then we get into these scenarios where management expects data in response to every opinion imaginable. Which just doesn't exist.
It's fine to have opinions, but we need to make sure we communicate that as UX professionals, we do have experience and that experience should count for something when it comes to matters of UX.
In the case of responsive web design, this is simply how responsive web design works. I'd just list of the benefits of responsive web design (can vastly save money for the company, one site vs. two, reaches more customers, etc.) and ask if they felt those benefits outweighed the issue of resizing the browser while reading it at the same time.