Isn't 'however' the same as 'nonetheless'/'on the other hand''?

Language learners are often taught to memorize rules such as HOWEVER = NEVERTHELESS = NONETHELESS. All of these adverbs mean something along the line of "[FONT=&quot]despite something that you have just mentioned[/FONT]" or "contrast".

I'd therefore like to know if 'nevertheless' works in the following sentence:

The roles of men and women were not the same in the North American Indian tribes. For example, men were both participants and spectators in hunting rituals. Women, _____, were forbidden to participate.

A native speaker says that HOWEVER works but not NEVERTHELESS/NONETHELESS.

Actually, for this same blank. Some say that ON THE OTHER HAND works too. But it is contrasting two issues - men and women, and the pattern ON THE ONE HAND...ON THE OTHER HAND should be used to contrast two perspectives of the same issue. Am I correct? So, does on the other hand works in the above blank too?

Thank you very much

Tedwonny said:

So, does "on the other hand" work in the above blank too?

Click to expand...

Yes, it does.