There are a couple of issues with Am Ex. Firstly not all their cards are credit cards although if a charge card you still need to be 18 to have one.
however regarding age verification I can completely understand why eBay don’t allow them For this purpose. Amex allow parents to put children of the age of 13 and above on to accounts. In order they can build a credit score (parents obviously pay but having minors as authorised users allows them still to buy knives etc) I wouldn’t be surprised if this the same issue with some master card providers.