I think that's the point of him thinking that she's easy to read; he can tell that she wants to go on trips with family or friends. So he's proposing that their whole group can go on a trip together. So not really that surprising of a reaction from her.
Or actually, now I think about it, maybe he just meant in general, not with each other. Which is why he's surprised when Houjou assumes they'd be travelling together.
Idk if Houjou likes Youta, but I'd definitely say she considers him a friend or even close friend.
sorry..i don't get it.
'I hope we can all travel
together like a family someday'
This sentence, for me (as a non-native english speaker) only has two meanings:
1 - Travel together as a literal family...so married to each other.
2 - Family as having a friendship relation so close that you consider the other person as family even if you are not blood related. They haven't been in any kind of situation this kind of bond is formed only for friendship. So it doesn't make any sense on this context.
With this, along the comment on the next page where he is surprised that the trip is suddenly about him..then the situation is quite confusing.
Ok...I just read the raw, there is no reference to 'we'. It is true that the same sentence could imply oneself, but with the context is clear that the dude is referring to HER family, so I think the translation is not 100% correct here.