When the person you are talking to is refusing to meet you deeper

Perhaps they cannot? Impossible to force anyone to do so.
To be honest, I am not sure exactly what you mean.
I am guessing a deeper connection.
I try to take people as they are; some I have a less deep connection with.

Was in your shoes years ago. I was into him but he didn't feel the same way. We stopped talking for like 3 years. When we started to again he was ready for more.

Talking in terms of romantic interest or platonic conversation? Could you clarify please? I'm afraid this is slightly ambiguous... Given the wording.

Perhaps the person's anxiety of depths

I`m not sure what you`re meaning here.

Maybe they are incapable of it.

They may not have what it takes to do so.

Yes, that is when they psychologically plateau at a previously known stratum layer, below which they have never explored before, nor are they about to plunge below that layer for fear of their truth becoming over-exposed with the wrong person.