The problem of escapees to the West for the SED leadership was two-fold. Firstly, flight from the GDR undermined the legitimacy for the SED and was a sign both domestically and internationally that it was an unpopular regime. Accepting the escapees was tantamount to admitting that the GDR government was a weak government. Such an admission not only would this give the upper hand to the FRG's position that it was the legitimate postwar German state, after all there were much fewer West German asylum-seekers in the GDR, but such an admission of weakness could lead to further domestic disturbances such as that of 1953.
Secondly, the social profile of those fleeing to the FRG tended to be educated and productive members of GDR society. West Berlin's openness prior to the Wall had allowed these Germans to easily escape to the West. This amounted to a brain drain in the GDR as these individuals could not be easily replaced. The perception that the GDR had fallen behind its Western counterpart was a source of acute crisis for the SED in light of the explosive economic growth of the FRG following the currency reforms of 1948. Allowing productive members of its population to flee to the West was a tacit acknowledgment of an obvious reality, that the FRG's prosperity had exceeded the GDR's planned economy, which the SED sought to deny. Furthermore, allowing members of its population to flee to the West created a demographic crisis that would forestall any attempt by the GDR to correct this economic discrepancy.
Even though the Berlin Wall and the clamping down of the inter-German borders was a propaganda disaster for the GDR, for the SED leadership it was the least-worst alternative to admitting weakness and their inability to catch up to the West.
Additional question, if I may - what was the GDR's justification for not allowing people to leave for West Berlin, and even going so far as to shoot people trying to flee the GDR?
The wall was built in august 1961, before that a huge number of people left for the west, often qualified people left. In the late fifties farmers began to leave in large numbers, as the GDR switched its agriculture to collective farms. Between 1950 and 1961 about 2.6 million people left east germany for the west; that was out of a population of 17 million.
http://www.berlinermaueronline.de/geschichte/fluchtzahlen.htm