Japanese Language Question

Daraちゃん said:

I wanted to say in Japanese: "We have a lot of things in common!" And so I said, 私たちは共通点たくさんありますね！" And to my surprise, the Japanese person I said it to corrected me, saying she understood what I was trying to say, but said it wasn't the right way to express what I wanted to say. I was discovering the person I was speaking to had a lot of the same interests and hobbies as me and I was simply trying to point that out.

I feel like there's nothing wrong with my usage.

Who is right here?

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