The words "each" and "every" can be used with singular nouns that are part of a group. However, there is a difference. When using "each", you're focusing your 100% attention on the individual (one person, one thing).
Example 1: "Each person who came to the party, brought a present." The party had a lot of members, and each one of them brought a present.
Example 2: "Each city in Europe is beautiful." Again, there are a lot of cities in Europe, but each one of them is beautiful.
"Every" refers to a group of individual objects or people as one group altogether. Now the 100% attention is on the group.
Example 1: "Everyone who came to the party, brought a present.". Here, a group of people came to the party, and all of these people brought a present.
Example 2: "Every city in Europe is beautiful". All the cities in Europe..., we're making a generalisation about the cities in Europe (as a group of cities).
So, you use the one which fits to your sentence and its context the best. If you want to have all the attention on the individual, in this case "each man...", you use "each". If you prefer to focus on the "group of men" more, then "Every man..." works well.
I hope it helps!