There is no connection between the three songs beyond the word "man" being in each of their titles.

In the first, Jewel is not clear on the word "man."

This may be compared to usage of the word man to humans in general.

Second issue: What do you think of the people who want to take the word "man" out of common words?

Parliament voted to removed the word men from an article of the law that applied to voting.

The word man had entered his mind during the self-examination and felt right to him so he'd applied it to himself.

The word man is used to mean any adult male.

This semantic shift was parallel to the evolution of the word man in English.

He said "You are a word man; you care about words."

The word 'man' is very unclear but I cannot see how else it could be read.