That's probably because people pay online only at a very limited number of places they trust, and it's easier to solve issues with the local merchants directly.
Another reason might be, that many online payments are made via direct bank tranfers / SEPA, which can be both, fee-free and instant, across the entire EU.
Essentially, everything is based on trust. Nobody puts his debit / credit card details into a form of a website he never heard before, and nobody risks his business reputation if he has managed to earn it.
what makes you think debit cards are less safe than credit cards? as far as I know here in EU all debit cards are smart cards with PIN code protection, what exactly is the unsafe part?
are you confusing debit cards with magstripe cards?