Not sure, but it is possible that I may have been the mom you mentioned, as I've commented on martial arts for my son several times. I totally understand your feelings of not wanting to "mess up"...how do you encourage without pushing too hard, how do activities get chosen, etc. You sound like a good mom who's trying to navigate all the "stuff" society is feeding us. I just want to say that first, every child is different, different families have different values, expectations, financial or time constraints, and every child has a different experience, temperment, maturity level, desire to draw from, so I don't think many "blanket" statements on what you should or should not do will be right. We can only say what works for us and our families.
I started my oldest son in gymnastics when he was 3 years old for a couple reasons: it was the only AFFORDABLE thing for 3 year olds to do, I was in my third trimester of a high risk pregnancy and not able to play as much as I'd like with him, was concerned about how he'd feel when the baby came and wanted something that was "just for him" to make him feel special and look forward to. It was 2 days/week, and we pulled him out after the 5th class because although he was keen to go and play, he wasn't interested in standing on the line, waiting his turn, and he couldn't for the life of him understand why they'd leave the trampolene and move on to something that wasn't as exciting, like walking on a board. Fail. We weren't angry with him, and the coaches were remarkably patient, but we realized he just wasn't mature enough to WANT to follow directions. He'd be just as happy if we bought a little floor trampolene for the living room, ya know? So instead, I put him in a 2 day/week mother's day out program (his "school") and he felt very big and happy to go to that. We also went to Bible study once a week and he liked going to his class at church while I was in mine. That gave him some social time, helped him be independent and understand that mommy always comes back, which helped his confidence grow because instead of worrying about me he knew he could forget about me a few minutes and go explore.
We put him in swim lessons that summer at the local recreation center. At that age, it's like 1 teacher to 3 or 4 students, and he did fine. When he was 4 years old, we realized that he was very active, loved to balance and loved to be tested on balancing, loved to "fight" with his daddy, a few little things that made us think he might be naturally good at martial arts. I shopped a bunch of schools (I was looking for style, watching and listening to the teachers, watching their students---because while a teacher can be on his best behavior and put on a show for a new parent, the students won't change). The quoon (school) I chose, I honestly disliked the sifu (but I wasn't looking for a friend, I was looking for a good teacher), but I really respect what a great teacher he was for my son and loved the discipline, tradition, confidence, and desire to grow that he instilled in my son. My son did awesome, thrived, loved Hung Gar Kung Fu. What we did: first, I showed him the old version of Karate Kid because Mr Miagi is very preachy about not fighting for fun or to be mean, but really pushing that it is for defense. I said "Would you be interested in this?" and he was. I shopped a few schools, then let him visit the 2 that I preferred. We agreed on the one he went to, which he started at 4 years, 4 months old. He would come home and practice everything he did in class again at home. He'd lead mom and dad in the work out: he'd say "You the Joseph, I the Sifu (teacher)" and he'd lead us through the warmups, the drills, and then whatever he was learning at the time. We're very proud of him, how good he was, how much he grew, and how he applied it in real life scenarios a few times. We loved watching his posture change as he gained confidence, how he'd introduce himself to a new child or adult, all kinds of things. I can't say enough about how wonderful it was for him, something he loved going to for 2 years, 2 and later 3 times a week (until we moved away). But that was him. I did see some kids that tried it, did ok, and then dropped out. I did see one little boy who was a little less mature and had some behavior issues at first, was sloppy for a little bit, and then he started doing well with it. That little boy's dad was deployed and he was in it because the mother had several children and needed help with discipline, and we did watch him blossom and improve. Another little girl wanted to join, but then when he signed her up for that first month, she refused to go out on the floor and refused to leave her dad, she'd lay down. He was embarassed, but the sifu told him to just leave her alone: no pushing too hard, and no coddling either. The last couple minutes she did come out. The next time, it only took her 20 minutes to go to the mat. By the end of the month, she was doing well, and later became my son's greatest competitor and good friend. It took some pushing. I became friends with her dad and he said he'd paid for the first month, and she was going to come that one month, and if she didn't take to it then he'd take her out. I agree that's what needs to be done. Don't sign a commitment contract for more than 1 month until you know if your child likes something, even if it was their idea to try it out. If it's not your child's idea, then maybe just do it at home first and see if an interest develops.
When Joseph was 4 1/2yrs old, he joined a soccer team. It was fun, it was FUNNY, but it was a bit of a mess. He didn't really learn much but he made a really good friend that he's had for years. We didn't go expecting him to become a prodigy and allow us to retire early since he'd be a World Cup star, we went because he said he wanted to. We didn't bother for 2 years after that though, and did other activities like horseback riding lessons, Awanas Bible club, swim lessons every summer (that's not a choice but a happy matter of fact, like school--something we "get to do, starting __ ") stuff like that. Now that he's 6, he wants to do soccer again so we signed him up for the spring season starting in March. We'll see what he does. But we also strive to just provide opportunities to see other things and have a little "taste" of it: the library, the recreation center, different events or places that have activities so he can experience different things, and develop interests wherever he sees fit.
My youngest is 3. We've found through visits to the galleries, museums, etc that he isn't much for paintings but takes a keen interest in the sculptures. We signed up for a free family art class once a month at a rec center, which we found through the library calendar, where we get to make art together as a family (fibers, clays, stuff like that). He has an amazing sense of balance and how to maintain his footing, a lot of both upper and lower body strength, and loves to "fight" with his daddy, is very natural in moving out of awkward positions when wrestling around with his brother, so we think when he turns 4 he'd love wrestling or a baby version of Brazilian Jiu Jitsu. He loves his Awanas club at church. We also attend a lot of free music events because he loves music. He really enjoys kindermusik as well (while his big brother, at age 5, seemed awkward and self conscious with it, so he just did the introductory class and didn't join up). We just provide opportunities for them to find interests, and then watch them and help them follow their bliss. I know this is ridiculously long, but hope it can help a little in showing examples of what we put our kids in and why, and how.....and that, in my opinion, once they show an interest and want to do something, and we join it, they need to actually try it for a few sessions (a month max) before leaving it. After giving it a good attempt, if they don't like it, give him some time and try something else.