Said differently, it's your bank that is choosing to do business with a child. If there are problems, you will be the one dealing with them. The vendor doesn't really need to make a rule against it.
Circumstances made it necessary for me to give my daughters credit cards at an early age. There is no way I would have given either of them a debit card.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.