Why super glue does not stick inside their own bottle?
From explainthatstuff.com:


  Why doesn't glue stick to the tube?
  
  Adhesives are designed to work when they leave the tube—and not
  before. Different adhesives achieve this in different ways. Some are
  dissolved in chemicals called solvents that keep them stable and
  non-sticky in the tube.
  
  When you squeeze them out, the solvents
  quickly evaporate in the air or get absorbed by the surfaces you're
  sticking to, freeing the adhesives themselves to do their job.
  
  Plastic modeling glue works like this. It contains molecules of
  polystyrene in
  an acetone solvent. When you squeeze the tube, the glue spurts out and
  you can usually smell the very strong acetone as it evaporates.
  
  Once it's gone, the polystyrene molecules lock together to make strong
  chemical bonds.
  Glue doesn't smell when it's dry because all the
  solvent has vanished into the air.
  
  Some glues (such as synthetic,
  epoxy resins) have to be mixed together before they work. They come in
  two different tubes, one containing the synthetic resin and the other
  containing a chemical that makes the resin harden. The two chemicals
  are useless by themselves but, mixed together, form a tough, permanent
  adhesive.


From sciencefocus.com:


  How super glue works
  
  
  The main ingredient in super glue is a chemical called cyanoacrylate, an acrylic resin that forms a bond (cures) almost
  instantly;
  The only trigger it requires are the hydroxide ions found in water;
  Traces of water are found on almost everything and in the surrounding air, which causes the glue to become sticky;
  It works best in moist conditions, although it is not advised to start gluing on a soaking wet surface.
  


Therefore the lack of water in the tube, or the chance of solvents evaporation, doesn't allow the glue to stick to the tube.

In other words: that strong smell that comes out when we open the tube's cap is due to the solvents evaporation, so once they're gone the glue sticks. If a superglue tube is left open for a long time (exposed to air, allowing the water to come in contact with the glue), it's impossible (or almost) to squeeze it out since it got stuck to the tube.