Are men's groups anti-women?
No. There may be an exception but I haven't heard of it.
Do men's groups have an initiation ceremony?
Some do, many don't. You can ask when you make contact. Accepting the confidentiality of what other men say, I wouldn't do anything I wouldn't be comfortable sharing with my family.
Are members predominantly divorced?
Probably not but there is no significant data. Overall I see the same desire to have a fulfilling relationship as men in the wider community.
Why do men join a men's group?
Greater self awareness, friendship, life perspective. Typically they say: "I'm not sure why I'm here ... I've never done anything like this before ... I have lots of women friends but not many, if any, men friends ... I think things could be different and better but I don't know how." After a while they say things like: "I don't feel odd or the odd-man-out any more. I feel OK about myself. I'm glad I came."