Asking Nathan out does not lead to dating him, he rejects you and ends your friendship if you do it while dating someone else. The full dating Nathan doesn't happen till in the 90's in day count at the ice rink, he will always reject you before for either not knowing you well enough or long enough or because you're dating someone else.
As for the day 60 comment in the guide, that's out of date from before the conflict events got changed in recent patches, some events will now trigger on set days earlier.