I want to say "X and Y coexist" in an article but my co-author repeatedly suggested wording it as "both X and Y coexist". We are not native speakers but her command of the language is better than mine. "Both X and Y coexist" sounds wrong to me. To be clear, what we mean is that X and Y coexist with each other.
Does it make sense to include "both" for emphasis here?
Both is definitely redundant here. It would have made some sense had these two separately coexisted with some third thing.
However, the kind of usage your co-author has suggested is apparently not all that uncommon . If you search google with "both * and * coexist" it shows a few million hits . See here : https://www.google.com/search?q="both++and++coexist" .
Quite possibly, people find the shorter version incomplete for some psychological reason. The reason I'm saying this is because Google also shows millions of example for coexist with each other which is also redundantly verbose (I doubt this redundantly verbose is a valid phrase either :-) )
Start with both.
Cambridge
both
predeterminer, determiner, pronoun (referring to) two people or things together:
Both my parents are teachers.
They have two children, both of whom live abroad.
She has written two novels, both of which have been made into television series.
In all these examples, both may be removed with loss of emphasis but with no loss of meaning:
My parents are teachers
They have two children who live abroad
She has written two novels, which have been made into television series.
In this usage, the determiner emphasises the commonality of the feature: teaching, living abroad, television series. It points to a feature that each person may or may may not necessarily have.
Things are a little different with your example.
Merriam Webster
co-
with : together : joint : jointly
coexist
In this meaning of co-, the feature of existing is necessarily shared, is joint. The addition of both adds no extra emphasis and is unnecessary.
In conclusion, your co-author is advocating an acceptable and common usage that is not wrong, merely redundant in your example, but your own position is concise, justified and defensible.
I want to say "X and Y coexist" in an article
You have not given the sentence in which this will appear:
"Although Z lives in temperatures that reach 300 deg. C, it is not unique: both X and Y coexist in this environment also."
The above sounds and reads better than the version without "both".
I would refer you to the excellent comment on redundancy by tchrist that you can find at Is the phrase “refreshing respite” redundant?
