就是【jiùshì】

就是 is 是 with 就 adding force: "exactly", "none other than". Before a noun, it picks out that one and no other.

Plain 是 or 就是

我是马克 just gives your name. 我就是马克 answers someone looking for Mark: "I'm Mark – that's me".

So 就是 needs a reason to single something out; as a plain description, use 是.

Stubbornly

Before a verb, especially with 不, 就是 says someone simply will or won't do something, whatever anyone says.

It's just that

At the head of a second clause, 就是 adds a reservation, like 只是.

Agreeing

就是！ or 就是嘛 on its own is "exactly!", "right!", agreeing with what was just said.

就是…也 "even if" is a separate frame with its own point.