Learning to drive is a really valuable, useful life tool. It opens up opportunities for work, travel and most importantly independence for both parent and child.
As we have always lived rurally, I knew we would have to spend hours of our lives dropping off and picking up children. A price we were happy to pay for living where we live. However all kids (3 DC and 4 Sdc) know that at 17 all were expected to learn to drive .
We've taught 6 of them on the smaller family car as it's easier vehicle to learn on.
It's complete bollocks to say the insurance is really expensive. Our kids were added as learners on both stand-alone policies or the main policy as learners. Never paid more than £30 a month for additional cover.
As for worrying about the car, one of the reasons learner insurance is not expensive is because learners are not a huge statistical risk. They are supervised by an adult, use L plates and people tend to be wary around them and ime as a supervisor to 7 learners over the years, most other road users are kind and tolerant.
Lessons are great but it's practice that gets you through the test and makes you a safe drive. Most of mine have had between 4-6 lessons and 3 months practice .
I think you are looking for reasons to say no without actually having a logical reason to do so. YABU.