Your stories about how to be present for a problem you can't solve
Chuckled reading your examples of learning to draw or learning Greek together, because I'm reading this while sitting gingerly in my bed, already feeling bruises start to form from a snowboarding lesson I decided to do with my 9yo son tonight. (I am so going to regret this tomorrow!!) I was joking to him though that this is kind of a tradition from my side of the family, or at least something I got from my dad -- pick an activity neither of you have any semblance of competence in, and then go for it and count it as bonding. (My dad's most famous example is bringing college-age me to the top of the mountains over Albuquerque, getting on mountain bikes, and just...pointing them downhill. Neither of us had mountain biked before; it was terrifying, and I will never do it again, haha. But it lives in infamy and I love that we tried it/he thought it was a good idea).
being a friend/mentor/parent during a crisis: it's almost always better to not offer a solution but to listen and let the person going thru the crisis figure it out. but, it's oh, so difficult. the consequences of problem solving for others are many. say a loved one is going thru a break-up and wants you to sympathize and you do. what happens when they get back together with the
'bad guy' that you bad-mouthed right along with her? you might have talked yourself out of a relationship with your child or dear friend when you were merely trying to commiserate. it's also not a great idea to be your child's confidant in relationship issues, btw. you're not their best friend. you're a safe haven, i hope, but they should seek such counsel from others so a parent may continue in the role of safe haven.
as for waiting things out while others find their footing, this is a win-win. when we jump in with solutions, we rob others, especially our kids, of their dignity - of the knowledge that we are dead sure they are smart enough to figure out what's best for them. you do that too many times and you create a person who will never be sure of his/her own decision making ability. that's not what i want for my child. we do that gradually over their lives, like letting out the string on a kite, beginning with what outfit they want to wear at age 3 and going without a jacket on a cold day at age 6 (and paying the consequences), and so forth. so, at age 16 we can trust them with car keys and then with our credit card at college or on a high school trip. we offer experience, they earn it.
if we do this properly, by the time they are adults, we are echo chambers for their good decisions, for the life decisions they want to discuss with us but for which they already have the skills to navigate. fortunately, as parents, we get to start out with the smaller problems and issues of babies and toddlers (in the normal world) and learn as we go before we get to the larger problems and issues of our growing kids.