Why doesn't glue stick to the inside of the glue bottle?

Because it needs air to make it dry and sticky.

Another great and puzzling question. Why doesn't glue stick inside of the glue bottle.

Glue on paper: As the glue connects with oxygen it becomes sticky and if left to dry in this oxygen it becomes hard and keeps multiple things together.

Glue inside the bottle: Glue doesn't stick inside the bottle because the chemicals within the glue is triggered by oxygen (what we breathe) so when the glue bottle is opened it triggers the chemicals to make it sticky. That's why if a bottle if left out with no cap the glue becomes quite hard.

Glue won't completely stick unless it's dried, and because inside the bottlee, the glue is still air locked in and not dried, it doesn't stick.