He was unsure a few months ago, now he says I'm his girlfriend?

Anonymous
I’ve been dating this guy for about 6/7 months. We’re 9 years apart and I don’t notice the age difference. We get along like a house on fire, I know his friends, his family know about me but we haven’t been able to meet due to Covid. A few months into dating, he asked to make sure that we’re not seeing other people. A few months ago I was anxious about what we were - he hadn’t asked me to be his girlfriend and I thought this is something that he would’ve wanted to do. He’s traditional, wanting something serious such as marriage/family. We had a few talks about the direction of our relationship, he said there were a few things he was a bit concerned about, a few things we maybe didn’t have in common (he’s very risk-averse and overthinks everything).

He’s studying medicine so after that conversation he said he would decide at the end of his exams, his exams have finished now. So the other night on the phone, I told him that I wasn’t quite sure whether continuing to have sex with him was a wise idea as we aren’t boyfriend/girlfriend. He was confused that I said it was casual. I said ‘well, we aren’t in a relationship’ and he said ‘you are my girlfriend’ I’m certain he went onto say ’I thought we’ve known this since we started dating’ so I then asked him ‘well if I was to meet a new friend of yours that I haven’t met, would you introduce me as your girlfriend? And he said yes. Unfortunately, he has to repeat his exams so I may not be able to see him for a while, I do need to clarify that he actually meant this.

I just wonder why he had this hesitancy a few times when we had the discussion a few months back though? There was even a point where I suggested we should end things because he wasn't so sure and he agreed. Maybe this is natural though and a reflection of his risk-averse attitude about things. There were just some uncertainties on his part. He said he could've been overthinking it. As a result, it sort of made me more anxious and I suggested we should end it.
Updates
+1 y
It made me more anxious and I suggested we should end it. We both kind of came to our senses and he suggested we have a talk. To be honest, since then, I've noticed we've become far more emotionally involved and I feel closer to him. It could be that he's felt that too and made the official decision in his mind too.
He was unsure a few months ago, now he says I'm his girlfriend?
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