Give it up. He's only saying that the church that is at Rome has or should have preeminence among all the smaller churches in and around Rome, just as the church at Thessalonica would have preeminence in the area around it.
And Ignatius coined the term "catholic" but Pontiff Constantine capitolized that term and then capitolized on it for the title of his new Roman church. What Ignatius meant by "catholic" and what "Catholic" has come to mean are quite different, so different that he must still be turning over in his grave at the misuse of his word.
He was writing from Antioch. That's not near Rome. So stop trying to rewrite History.