Okay apparently I'm going to do a study on this introduction, because going back to it? Especially knowing more about Hakuba via more recent Magic Kaito chapters? Fascinating stuff.
So. Hakuba's introducing himself, and he starts out by bringing up "My father spoke of you often" and "It seems you're a very sharp detective." Both of those are positive!
Hakuba is... high society, compared to Hattori simply hanging out around high ranking people and treating them like normal. Hattori argues with Kazuha in a very down to earth way, while Hakuba knows how to drink tea and probably how to set the table with a full set of cutlery (or at least how to use them).
So, Hakuba using their fathers to introduce himself is, to him, a normal enough way to say "I've heard good things about you, we're similar, I hope we can get along well."
What's more - Shinichi realises that, pretty quickly. Even if they hadn't met previously, he'd have been able to figure out by the words being used, that Saguru's father knows Heiji's father, or that they're in the same business.
If anything, I'd say that this slight culture clash is the second step of things going wrong between Hattori and Hakuba here, right after Hakuba being present at all, since Hattori had wanted Shinichi to take his rightful place where Hakuba is currently sitting.
Unfortunately, it gets worse from there, and I'm gonna go into it.