When people ask if you are a couple and you aren't, so awkward, how to handle?

Anonymous
i am dating a guy and we talk all the time but we aren't boyfriend and girlfriend. I like him but I don't know if I want a relationship with him and I didn't think he wanted one with me even though I do think he likes me.

today we were getting drinks together, of course being very touchy and laughing a lot and I guess our body language looked coupley (we were leaning in, our hands were on each others legs, and in the street we hold hands, cuddle, kiss, etc) because this girl next to us asked "So, how long have you guys been a couple? I mean dating?"

His and my eyes met in this weird way and he goes to me "you answer that" and I had nothing to say so he goes to her "Yeah we're just friends and messing around with you. Actually, I'm her tutor and she's my student, that's how it really is"

Then I told him he should just tell her we are related and he started laughing and we were both cracking up with each other.

After we left he mentioned it and said I seemed unhappy when he said the "friends" word.

But he has said we are "dating" before and we are going out again in a few days.

So, what gives? does he like me? in general I think he is very into me.

and he does act like we are a couple when we are together. we hold hands, he kisses me, cuddles me, calls me pet names, talks to me all the time, etc.

Updates
+1 y
after he told me I don't like that he used the friends word and asked if we are friends. He also started talking about how "these things are complicated" what gives?
When people ask if you are a couple and you aren't, so awkward, how to handle?
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