Would you be willing to elaborate?
Personally, I think with what you said, it's a little bit taking a deep reach on what he meant. One that leans on towards the more negative side of course.
Let me address it one by one:
a) What did Arata mean by it?
If we are to take in his character and how his mind works from how he really acts, I'd say he was describing how when you try to do cling on towards other people that way, you'd share those with "special" people. Like of course, lovers. Sort of that those actions are meant to be reserved towards particular people and definitely not something you can just ask out of someone randomly even if you are friends. So you know, it is quite conservative, but thinking as how he was brought up and the society in Japan, they would definitely reserve those types of actions (hugging, handholding, all those physical ones) to more special people and moments.
b) The concept of siblings, parents, other (extended) family
To judge Arata from his statement and connecting it towards his views regarding family, I'd say it's quite a very bog far deep reach. Why? Because first off, contextually at hand, Arata and Chizuru are NOT family. They're just friends. To say that he doesn't know or understand the concept is just reaching out towards something that has no tangible backing. As presented in the story, he's just addressing the relationship between them. They are not a couple, far from lovers (at the time), that's why they shouldn't engage on those kind of actions.
c) Concept about non same-sex relationship (?)
This part... I just don't get? To say that he doesn't understand heterosexual relationships is... weird... I'd say I probably may have just not understood it. I'd like for you to elaborate it though so I can get a better understanding of your view.
d) To conclude:
I just think it's unfair to judge his views on multiple facets based on a singular statement that fitted the context at hand. He just basically said, "Chizuru, we can't do that because we are not lovers." And that's what Chizuru took from it.
These are all personal understandings and comprehension so, feel free to judge it.