I think they're both understanding this date and relationship are over, but the therapist is down to help miharu psychologically a bit before they don't see each other again (at least not in a courting way)
The guy has been legitimately helpful to both nozaki and oshiko when he's in his lane as a therapist, plus he's one fictional depiction of one therapist, don't let him turn you off of therapists in real life
No lie I could see oshiko being a compulsive liar in order to smooth over things that embarrass her, things that are so mild and only embarrassing in her head
I plead the 5th for my experience with this mentality