Where is "here"? I agree with your parent, in places that support Apple Pay/Android Pay/PayWave/contactless payments (e.g. Singapore, the UK, and surely more that I don't know), cashless is easily more convenient.

In places that don't have contactless payments, cashless may be less convenient but contactless is probably on its way there so your argument seems like a bit of a straw man. At any rate, I'm sure it can be agreed that contactless cashless payments are more convenient that cash ones.