As discussed on this question the Soviet Union heavily regulated the travel and emigration of its citizens to foreign countries, with the border heavily fortified with machine guns in some areas to prevent unauthorised citizens from escaping the country.
But what was the official rationale for this policy, either in internal or external media? Did the Soviet propaganda somehow explain why one cannot simply leave the country?
There was no general justification, and formally travel was not prohibited.
Emigration. On this I have heard one justification: In Soviet Union many things were free for all (education on all levels, medicine and other social benefits). In theory every person was expected to "contribute to the society" in return. So the argument was : if you emigrate then you do not return what society spent on you. At some point, when under the pressure from abroad, limited emigration was possible, they charged an enormous sum of money to give a permission to emigrate.
Simple travel, for vacation for example. Soviet citizens were not expected to possess any foreign currency. Any currency speculation was a serious crime. (The punishment depended on the amount, but it could be death sentence). So a person could not just say: "I want to go abroad for vacation". S/he had to ask for some money exchange. So one had to apply for "permission to travel", and some (very small) number of permissions were indeed granted. Who could travel and for what purpose was strictly regulated and the rules were different at different times.
No one would dare to claim that s/he possesses foreign currency. And very few people would dare to say that they have relatives abroad or that some foreign agency invited them. And if you say so, the matter will be investigated, and you may eventually obtain a permission or not. One common reason to decline an application was "there is no guarantee that the person will return". (See section 1 of my answer). For example they normally would not permit an unmarried person to travel to a scientific conference on this ground.
So in theory there was no complete prohibition, and thus no justification was given or needed. In general, the Soviets never accepted the principle that "everything is permitted which is not explicitly prohibited". The general principle of the Soviet society was the opposite: "You need to obtain a permission for every move". This was a totalitarian society.
EDIT 2. There was a whole genre of adventure fiction for children, about glorious border troops (пограничники) who were catching the spies. It was a kind of revelation to realize at a later age what the main function of these troops was.
EDIT. One general remark on the questions "about Soviet Union". Soviet Union existed bout 70 years and the situation changed. My answer addresses the situation from 1960 to the middle 80s, of which I have personal experience. Relaxation of restrictions began in 1989.
The official position was that there was no limitation for freedom in the USSR, including freedom of movement. On the level of Constitution and laws it was so.
But there were many instructions that were set (not published!) by many state departments. They were even more powerful as the law, for they were set AFTER the law. Practically every state organ could develop such instruction.
And these instructions REGULATED the movement across boundaries. And the result of regulation was practical impossibility of realization of rights given in law.
One of the last declared targets of Gorbi was "law state" - the state where people will be subjects to laws, not to unknown, and often even secret, instructions.
Travelling as a tourist was not officially prohibited, but the thing was, you could not travel alone. You always should get an organized tour, with a guide etc. The main problem though was to get a tour voucher. It was easier for tours to Socialist countries, and much harder for tours to Capitalist countries. You also had to exel in something, usually at work to be awarded a tour, because the number allocated per organization was limited (and different for various enterprises). Possibly, there were also sold tours, but very expensive.
Many people had access to the secret documents so they had no permission to travel (but were paid more for classified access).
