The main example I've seen cited as to why cleric spells would be effected by an antimagic field comes from the sage advice compendium:
Determining whether a game feature is magical is straightforward. Ask yourself these questions about the feature:
- Is it a magic item?
- Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
- Is it a spell attack?
- Is it fueled by the use of spell slots?
- Does its description say it’s magical?
If your answer to any of those questions is yes, the feature is magical.
I think this misses the point. The question being asked here is not if a cleric's spells are magical, but whether cleric spells fall under the exception made in the antimagic field spell:
Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can't protrude into it.
The Players Handbook specifically calls out where a cleric's magic comes from:
Divine magic, as the name suggests, is the power of the gods, flowing from them into the world. Clerics are conduits for that power, manifesting it as miraculous effects. The gods don’t grant this power to everyone who seeks it, but only to those chosen to fulfill a high calling.
It says Divine magic is the power of the gods.
This questions seems to be answered in the cleric description.
If a cleric's spells are the power of the gods, then I don't see how they would not be created by the gods. If they are divine, they would not be subject to an antimagic field with the stated exception carved out for magic from deities.