My 5.5yo daughter is very shy, so I've been pushing her into hobbies to help managing her shyness. I've talked about how being shy is fine, but it's something to work on, otherwise she'll have a really hard time making friends. I'm shy and told her about that.
I took her to a gymnastics class (we do gymnastics together at open gym), but she refused to join the class. I said if she does one activity (even just a game at the end), I'll get her ice cream. We spent the time sitting on the side.
She didn't do it, so I figure no ice cream then. She's pretty mad. I'm not mad with her, but just of the opinion that we had a deal, and if she wants the reward, she needs to earn it.
Too harsh? Too soft? Alternatives?
EDIT:
So I took a two prong approach. 1. hard rule for no screaming at me or arguing. 2. we can just sit and watch, but if she joins, we leave after 1 exercise, each time slowly staying longer. She seems to feel safe when she's in control of when she leaves, which makes sense. Seems to be working. She expressed that she was surprised the kids and teacher were nice to her and loved it more than her art class.
I'm not 100% sure why she's so afraid of other kids. Maybe something happened at school I don't know about, but she's way less anxious about the class now.
The childhood me would stay at home all day, to the point adults gave me nicknames. I don't know about your child, but when I was five, I enjoyed fiddle with/take apart things, watch insects or watch nature in general, and hiding in a corner imaging a world.