Why is the plural version of deer identical to the singular version?
If mouse became mice, then why did the singular deer not change to something else in the plural?
Learn English – Why is the plural of “deer” the same as the singular
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This is all down to the fact that English is a language of acutely mongrel lineage. It has substantive roots in Celtic, Romance and Germanic languages (to name a few) and a grammar that lends itself well to the adoption of "loan words" (non-native words adopted into the native tongue.)
The "standard" means of pluralising a noun is to append -s, with some conventional variations (eg -f becomes -ves, -y becomes -ies) for convenience in spelling and pronunciation.
However latin-based words tend to pluralise in the latin fashion, so for example bacterium becomes bacteria, and cactus becomes cacti. Similarly greek-based words will adopt the equivalent pluralisation appropriate for the original root.
Still other words of Saxon or earlier origin have lovely, earthy plurals that defy the "conventions" due to their traditional forms being maintained. Geese, Mice and Children owe their unusual conjugations to their ancient roots, and to the fact that they are common words whose everyday repetition keeps them from slipping into bland conformity.
In my experience, words which do not pluralise are those which relate to herding, hunting and the counting of animals. These words tend to be saxon (germanic) or celtic in origin owing to the presence of farming and hunting in Britain long before the Norman invasion. This can be inferred by the fact that sheep, cattle and game do not pluralise, while whales, sparrows and elephants (seldom hunted or farmed in Britain!) definitely do.
I suspect these tend to be a contraction of the traditional counting forms for such cases ("head" of cattle, "brace" of partridge, "shoal" of fish) but this doesn't really answer the question of why such plurals take the same form as the singular. It could be that when counted in such a way, the animals being counted were considered an uncountable, continuous quantity (similar to water or money) that could only be "counted" when quantified with their associated counter, so cattle would be rendered an uncountable noun by its quantifying counter head. It's interesting however to note that bird pluralises to birds, while aircraft does not pluralise.
Sadly for the non-native speaker, this makes learning the "rules" of English an arbitrary and frustrating affair. However, spare a thought for the Japanese, who do not have plurals for any but a few unique nouns, and must instead learn a separate counting-suffix and corresponding character (kanji) for almost every class of noun imagineable. There are in fact entire volumes of the things, and it would be nigh-on impossible for any person to learn them all. Wikipedia lists a choice selection.
The first sentence features ellipsis, that is, the omission of elements which are recoverable from the linguistic context or the situation. A full version would be on both the sender side and the receiver side. Once we reach the end of the sentence we can recover side and place it in our minds after sender. That’s not too difficult to do because the missing element occurs within a few words. However, some readers might be uncomfortable in performing that little bit of linguistic gymnastics, and that is presumably what the reviewer felt.
The answer to your question is that both sentences are grammatical, and both convey the same meaning. If you think your readers might have difficulty with the omission of side after sender, then use the version that uses the plural: on both the sender and the receiver sides. Alternatively, use the full version of the ellipted form with the singular: on both the sender side and the receiver side.
Best Answer
It's a matter of historical origin and subsequent development.
In the oldest recorded English deer belonged to the neuter declension, which did not have a distinct plural ending in the nominative and accusative cases. (It is believed that this declension did have plurals in Proto-Germanic, but they disappeared before English or any immediate ancestor was written down.) At that time there was no ambiguity, since the determiners accompanying these nouns did change in the plural.
Later, when the Old English endings were mostly lost, the majority of these neuter nouns acquired 'regular' plural endings in -n, eventually superseded by endings in -s: wīf, for instance, became wives in the plural. A few, however did not, and deer is one of these.
It is often remarked that all these nouns with invariant plurals denote animals, deer, sheep, fish, swine, which are either herded or hunted; and it has been suggested that both the 'mass noun' sense with herd animals and the custom of referring to all hunted animals in the singular (we hunt bear, lion, and elephant as well as deer) helped inhibit plural regularization.
ADDED: See the second edition (1954) of Jespersen, A Modern English Grammar on Historical Principles, Part II SYNTAX (First Volume), Ch.III The Unchanged Plural (pp. 49–69), especially 3.1–3.2 and 3.71.