Jim lots of EU citizens live in non-EU countries that does not make the country they live in eligible for EU membership.

Uncomfortable facts that get in the way of your Prof's train of thought:

The country that joined the Common Market in the 1970s was the United Kingdom of Great Britain and Northern Ireland. Should Scotland be idiotic enough to leave the United Kingdom in 2016 then the United Kingdom as an entity does not disappear it will still exist to all intent and purpose. It was the United Kingdom that has been the national entity that has signed up to all subsequent EU treaties and agreements - So as far as the EU is concerned Scotland as a nation simply does not exist and as such cannot be considered a member.

Any country that is offered membership must go through strict and rigorous procedures and it must meet certain criteria. This takes time and without a recognised currency backed by some form of formal currency union independent Scotland must start at the bottom of that ladder, exactly as Lithuania had to.

Any country having gone through that "cumbersome accession process" then has to gain the unanimous consent of all existing members before being granted membership. Musket mentions "Catalonia", well Spain is not alone, excluding the United Kingdom, I can think of at least six other EU member states who in voting in their own national interest would block independent Scotland from becoming a member.