In the case of annual reviews we have such a wealth of evidence they do not work it is amazing so few companies have actually done away with them.
One of the reasons I have proposed the concept of CAO (Chief Agile Officer) is for situations such as these where someone at the top level of the organization can arbitrate using the entire organizational as a lens to determine best courses of action. It sounds like you are both on the same organizational level so it would help to appeal to a higher management level in instances where two of the same level cannot come to a satisfactory conclusion.
One of the things I have noticed during this time is, as Agile (and especially Scrum) have become more mainstream, the quality of individuals calling themselves scrum masters and agile coaches has become more variable.
When someone mentions “waterfall has always worked for us”, I believe this is an example of Type Three error. The real question – has waterfall been optimal? The example I always give is that the covered wagon was successful for transportation, but when I look out the window of a plane, I don’t see any crossing the prairie. In the case of those applying the values and principles of agile properly there is little doubt as to which is the airplane and which is the covered wagon.