Why should we stay in an undemocratic organisation?

You have been misled.  The EU is a fundamentally democratic organisation. 

The EU is democratic and accountable at every level. Any claims otherwise would be hilarious except for the fact that some people believe them.

It is made up of 28 democratically elected Member State Governments, acting jointly with the directly democratically elected MEPs in the European Parliament.

The MEPs and Member State Governments oversee the work of the European Commission, and appoint the Commissioners.  The Commission is the EU's Civil Service. The Scottish Civil Service is not elected either and to pretend that the EU one somehow should be is flatly silly.

 Many of the problems we, in Scotland, face are not due to the EU’s lack of democracy, but instead due to UK priorities, often failing to work constructively with our EU partners. Poor outcomes are due to who speaks for Scotland in the EU.  As an example, an independent Scottish Government would have prioritised our fishing industry in a way that the UK Government simply did not.  Scotland’s fishing industry was described all the way back in 1970 as “expendable" by the UK Government in a leaked foreign office report.

The EU is not perfect, but it is democratic.

If you want to know more about how the EU functions click here.