Dear Hmm- If he has been her student for NINE YEARS and is still not ready to do a simple solo, then it's high time he changes instructors because she must be awful.
Dear Anon- Wow. A man who is eager to do a solo? That's great! It means that you have some confidence in your dancing, which is half the battle for any leader. Does your studio go to competitions? That may sound daunting, but don't panic. They split it up by dance category, age category AND skill level. So you could dance with other students at approximately your own level.
You are absolutely right in wanting to challenge yourself with a "solo" or with a competition (or with both

. We find that our students advance much quicker with a deadline and a goal. Additionally, most of our students find their dancing to be more rewarding when they have a focus...there's a certain amount of fulfillment from knowing that you set a goal, practiced, and conquered (so to speak

If you are uncertain about your instructor's desire to do a solo with you, you might try asking her if you could do a solo number with another student...this has many benefits including that practice time with another student is FREE while you have to pay your instructor to practice

Your other option: change teachers. At least ask about taking some "exchange lessons" with other instructors...it might alert her that she is brushing you off, or you might find that she's not your ideal teacher after all. Consider studios that actively attend competitions!
Best of luck! M
championdancesport@comcast.net