Where does the belief that seeds die before they turn into a living plant come from?

[Anomalocaris]

It’s the description of an appearance. Seeds do not appear to be alive. As Nudger implies, this sort of thing is common in mythology - life/death/rebirth.

Boru

I don't think the authors of the New Testament were implying that seeds weren't alive, I think that they said that seeds were first alive and then dead and only then turning into a plant, after they died.

I don’t think the authors of the New Testament has in mind any consistent definition of what it means to be alive that could be applied to measure all things, nor would they think such consistent definition useful.   They were in the business of persuading, not discovering or understanding.