The Scottish people do not think of themselves as Englishmen because they are not Englishmen.

Both Scotland and England were separate countries, each with its own nationality (Scottish and English). They joined together, along with Wales, to form Great Britain. Great Britain (Scotland, England and Wales) along with Northern Ireland, together make up the United Kingdom.

Just as in China there are Zhuang and Miao and Bai and Han peoples (among others), in the UK there are Scottish and English and Welsh and Irish people.

For more information I highly recommend the sources below.

Sources:

1. Barrow, Mandy. “What are the Nationalities of People Living in Great Britain?”, (http://www.woodlands-junior.kent.sch.uk/customs/questions/nationality.htm) 14-Oct-2009
   
   
2. Barrow, Mandy. “What is the Difference Between UK, England, Great Britain and British Isles”, (http://www.woodlands-junior.kent.sch.uk/customs/questions/britain.html) 14-Oct-2009