You've told them it's good to learn things. To stick at something difficult. Not to be embarrassed about being a beginner.
They've heard you say it. They have never once watched you do it.
What Actually Transfers
Children are extremely poor at absorbing advice and extremely good at absorbing behaviour. Everybody knows this, and it's still uncomfortable when you apply it to yourself.
What they're currently learning from you about difficult things is whatever you visibly do with difficult things. If they've never seen you be bad at something in front of them, the lesson they've received is that competent adults do things they're already good at.
Which is a reasonable inference from the available evidence. It just isn't what you meant to teach.
The Unusual Thing About a Language
Most adult self-improvement is invisible to a child. They can't see you getting better at your job. They can't watch you read.
A language is different. It's audible, it's obviously difficult, the mistakes are public, and the progress is undeniable across months. It's one of the very few things you can be seen to get better at.
And singing along badly in the kitchen is about as visible as learning gets. They'll hear you get it wrong, hear it change, and hear it eventually be right.
They'll Join In, and That's the Point
Children can't resist a song. If it's on in the car for long enough they'll be producing the phrases before you are, without anybody mentioning learning at any stage — which is worth watching on its own.
At that point you've stopped modelling a virtue and started doing something together. That's the version that sticks, for both of you.
What They'll Remember
Not the language. The image of a parent deciding to learn something as an adult, being visibly rubbish at it, and carrying on anyway.
That's a specific and fairly rare thing to have watched at close range, and it does more work than any number of conversations about resilience.
About Outputly
Outputly runs in the car, in the kitchen, on the walk — wherever your family already is. Not a study session behind a closed door. Just the thing that's on, until everyone is singing it.