1."Each of the men brought his favorite snack to the picnic." 2."Everyone who wants to be in the “Toughman” contest should pay up his life insurance."
First sentence seems right(does it?)but shouldn't we say "pay up their life insurance" in second one?
The first sentence is completely collect.
In the second sentence both he and their would be correct. In some cases he can be used instead of their when you know the gender to be male as you do here.
Use their if you’re not sure of the persons gender.
For example:
There is a mix of men and women. Their blood type is all different.
