Around the same age. It varies person to person for both sexes. But I'd say that's the average age when a person's career trajectory, habits, lifestyle, and life-goals start to take shape and become observable to others.
At 18-20, you have no idea what the person will become. At 25, you still don't completely know, but you have a better idea and more of an established track record.
The chance a person will undergo major behavioral changes once they reach 18-20 is like 90%. By 25, it's like 10%-15%.
Sure, of course as people get older they start to settle more into who they will eventually become, but what's that got to do with being an adult?
Anyway I've had about 5 different careers and lived in 4 countries and been basically on my own since I was 18. At which age did I become an adult? I'm 32 now and just started a new career about 5 months ago so I don't really understand your classification system for adulthood. Standard adult age is 18 in the western world, if people wanna say that those aren't adults or that they feel like a pedo by dating an 18 year old that's their own personal hang up.
18 year old women (and men) are adults. No reason to argue otherwise.
Edit:
Obviously everyone is not me and doesn't live a life similar to mine, but let me add a bit more. I personally like dating 18-22 or so because of exactly what you said. They don't have a career yet usually, they aren't overly serious about everything, they aren't stuck in their ways, they are open... I'm not trying to get married. I just wanna enjoy my life. If I'm in town for a few days why do I care about career or other stuff when I just want to find a cute local to show me around and have some fun with? I was in Barcelona a few days ago and went out with a young and beautiful Japanese girl, then I went to Beijing for a day and had tons of fun with a 20 year old Chinese girl, now I'm in Hong Kong and saw a 22 year old girl here last night. I'm not saying I'm sleeping with all of them or anything like that, but I will say that if I try to date a 25+ year old girl, they have a career and shit to do with their life, they have their own habits and routines... they aren't as likely to meet up for a date with a random dude passing through town on business...But what's a 20 year old girl got going on besides studying and hanging out in her dorm? Of course she'll come out have drinks and fun. Give me a girl that's spontaneous and exciting and not old (er) and stuck in her ways. These are generalizations but they fit your description based on age in a lot of ways, so I think I do agree with you, except I see these traits as benefits and you see them as drawbacks