What do you mean "spells require casts"? Spells are cast by spellcasters, but it isn't the only way a spell is used. ie: being crafted or used as a spell-like ability.
Sure, "spell trigger" is a type of magic item, but it is not a way you cast spells. Can you counter spell those? No. Why? Because it's producing a spell-like effect, but not actually "casting" the spell. Nowhere have you shown that something has said "triggering a spell through crafting is the same as casting a spell; except as follows" or anything similar, just that "spell trigger" is the name of an activation method
as such
Spells still don't require casts when they're being put in an item, because you haven't proved that trigger = cast
Doesn't the fact that the terms are explicitly called out as completely separate uses of a spell by the rules kind of mean that they aren't the same thing?
edit: as a bonus, the crafting section under each item type literally all literally specify what exactly it means to "trigger" the spell when crafting an item:
the section literally clarifies that triggering a spell means that working on the item expends a spell slot just like casting a spell expends a spell slot and nothing more than that. If you say that it does mean more you will have to show something that says something different than the magic item creation section, and even that wouldn't really do much because the magic item creation rules are primary. The whole "spells have primary rules" thing you're trying to do falls flat because spells have different rules based on how they're being used. They are either cast, or used in crafting a magic item, and those two things are not the same thingThe act of working on the ..(item).. triggers the
prepared spells, making them unavailable for casting during each
day of the weapon’s creation. (That is, those spell slots are expended
from his currently prepared spells, just as if they had been cast.)