I don't see what could mean "one by one pasta" in this context?
As was mentioned in naruto's link, いちいち is a word that implies that someone is saying or doing something step by step or giving a long-winded explanation, and helps convey the speaker's annoyance about this.
いちいち言って is basically "to annoyingly insist" or "to keep saying over and over (despite my lack of interest/despite how unimportant it is)" or "to go on and on about"
would thus be translated as something along the lines of
"It's strange to harp on and on, insisting on calling Japanese spaghetti a 'pasta' dish."
or adhering more closely to the Japanese word order:
"For Japanese spaghetti, annoyingly insisting on referring to it as 'pasta' is strange."