Rather than focusing on rules, get to the essence of the sentence. Try to speak that sentence in your native language. The author here wants to say that the woman's beauty attracts men. It doesn't scare them. Also think of it logically - can a woman's beauty really be intimidating to men!? Why will it scare them? Does beauty attract or does it scare someone?
The meaning of this sentence is that the woman's beauty attracts men,
it doesn't intimidate them.
The reason why a comma is present after
men is because the entire sentence contains two sections
She was beautiful enough to attract men and
but not to intimidate them. Both of these have to spoken with a pause between them.
Similarly, in the 1st example you posted, we can see that again, there are two parts in the sentence -
the man wore a long sleeve shirt which wasn't fitting him and
the shirt was worn fashionably. Again, get to the essence of this sentence. The man wore a misfitting shirt but he wore it in a fashionable way. Again, you will speak the two parts with a pause between them.
The reason there's a 'but' between the two parts is because the second part is indicating something contradictory to the first part. Take the 2nd example - in the first part, the author says the shirt wasn't fitting him well (shirt wont look good) but despite being a misfit, the shirt was worn fashionably (which made it look good on him). So you see, the meaning of the 2nd part is a contradiction to the meaning of the first part.
As I said, sometimes strictly following the grammar rules to construct sentences can be misleading. It can give you results which probably mean something else. So it is better to get to the essence of the sentence, try to understand what it means and how would you speak the sentence in real life. Converting English sentences to my native tongue always helps me understand the sentences better