byakko99008780-san, マイケルsan,
it's a good point, マイケルsan
It's very difficult to explain what are the real differences amongst だんせい, おとこのひと and おとこ,
but politeness is one of the factors.
Another is points of view, maybe. The word だんせい has せい which is written with kanji 性.
This kanji means sex, so this word だんせい and female version じょせい can refer to sex (i.e. "male"
or "female", or "masculine" or "feminin"), while おとこのひと literally means "person of man"
because ひと means "person" and おとこ means "man/male/masculine". Same goes to おんなのひと
where おんな means "woman/female/feminin".
It's difficult to say with a simple explanation "which word" is better suit, like マイケルsan says.
This is not just an issue of Japanese, but it applis to any language, I suppose.
If there's any possible adivce, it'd be "to understand each word with proper meanings and routs, not
just with translation". The translation for the だんせい and おとこのひと in those sentences
was "a man", but if you want to know those words more deeply, explanation above would help you.
Unless you understand any words "as Japanese" "with Japanese" (i.e. not translating into English),
the words with same/similar meanings will be always "same meaning words".
Hope it helps!
Natsuko(奈津子),
Team JapanesePod101.com