Listen, if your kid trusts you enough to ask for a burner, help them. Wipe your old phone or find something cheap, teach them about threat models, private browsing and factory reset, then teach them how to teach these things to other people. The only question you need to ask is, is this for you or for someone else, and you don’t ask who or why.
You don’t need to make the first conversation perfect, you need to make the next conversation possible.
@mhoye @emma I'm reminded of a friend, whose name totally escapes me for legal reasons, who explained to her teenage kids what Plan B was - an over the counter emergency contraceptive - how it worked and then absolutely did not give it to them b/c, as noted, legal reasons.
She may also have noted in passing where it was kept and that she had no idea how many were there should they or their friends accidentally take one.