Numbers 14:4 states that a man says to his brother that they should appoint a new head (of the Israelites) and return to Egypt. Who are these two brothers? And, if this is just a turn of phrase, why is it used here specifically and where else is such a phrase used?
I am not an expert in Hebrew but this seems simple enough for me. The Hebrew אָחִ֑יו is sometimes translated, to his brother, his brother, brother, his relative, another. In this particular verse it is translated as 'another' because אִ֣ישׁ (to one) אֶל־ (about) אָחִ֑יו (bother, or another) is the sentence fragment being considered. When combining these words the meaning is ‘to one another’. The same phrase is used in Genesis 37:19 (Also see Genesis 42:21, Exodus 10:23, etc.)
Here comes that dreamer!” they said to each other. (Genesis 37:19 NIV)
The meaning of 'each another' here is based on the root meaning of אָח a literal brother.
So here the meaning is:
And they said to each other, “We should choose a leader and go back to Egypt.” (Numbers 14:4 NIV)
In other words, the Israelites were rejecting their current leader Moses. They were saying to one another, in rebellion, that they should appoint a 'new leader' and go back to Egypt. Apparently they were not happy in the way Moses (and by inference God) was leading them through so many difficulties.