Your question holds a bolder statement than the quoted manager's.

The quoted manager states it is not needed, as if it would require a bigger investment to do an agile project compared to a non-agile project. It sounds like he would not mind going agile, he just believes the extra costs are not worth it. Which raises questions. Perhaps they never did agile before and they are expecting some adjustment costs.

But agile is not just about responding to new or changing requirements so the statement as quoted makes no sense.