President's speech to the "Muslim world" was directed at educated middle class Muslim liberals. Universalist respect and focus on human rights destabilizes Egypt the way Iran was during Carter.
Obama's speech in Egypt should be seen through a lens of economic nationalism. Obama's primary focus is domestic and revolves around domestic stabilization through industrial policy to crawl out of the economic depression. Everything he does will have to be sufficiently congruent with that goal. Internationally, we should begin to see Obama trying to save as much money as possible through creating conditions for withdrawing expensive troops and financial support.
Obama chose Cairo University as his venue to give a major speech to the Muslim world. This university was among the earliest modern institutions in the Middle East and its large size created one of the biggest breeding grounds for radical thought. Muslim extremism and pan-Arab nationalism had a lot of its roots among students in Egypt. The historically large campus (presently accommodating 200,000 students) allowed a diverse marketplace of ideas and vast radical social networks to incubate and give rise to organizations like the Muslim Brotherhood. Thousands of the faculty have been there for decades and lived through the consolidation of the Egyptian nation with all the social pressures involved. The previous and current faculty have influenced and been influenced by thought ranging from Ba'ath socialist nationalism, to Leninism, to Nasser's pan-Arabism, to religious revolution, and finally to Anglo-American liberalism. The brief period of Egyptian history as a nation state has seen the country as the van guard of attack against Israel, of briefly lived efforts at confederacy with Syria and Jordan, of leading efforts to reconcile and co-exist with Israel, and of becoming one of the biggest recipients of American military aid.
Obama knew exactly what he was doing by picking one of the biggest audience halls in the Middle East. The educated people who teach and study in Cairo university are used to major swings in national public opinion. These shifts are often the direct result of majority of academic elites being overcome by one particular idea and mood.
Unlike the Arab middle classes and academia in UAE, Saudi Arabia, Qatar, or Jordan, the Egyptian elites are more cosmopolitan and relaxed in regards to multi-ethnic societies, democracy, rights of women, and republican social constructs that separate church and state. Up to 10% of Egyptian population are Coptic Christians whose ancestors have been there since the Roman times. Egypt straddles the key point where Africa and Middle East connects and where endless European shipping passes through (with corresponding cultural influences). Cairo leadership is in control of a state that is as geopolitically important and pivotal as Turkey.
Obama knows that Egyptian elites and middle class are a few years ahead of their Jordanian and Saudi brethren when it comes to political cultural development. Talking to many of them directly was a very calculated move. Creating a sensationalist event and starting major media chatter on Arab talk shows and campuses was a perfect opportunity to plant seeds of a certain train of thought that can then infect middle classes in neighboring states.
The president's adoption of a respectful socially libertarian non-imperial message hints at an even colder geopolitical agenda than George Bush's. The venue to reach as many proto, pseudo, and actual Arab liberals as possible has potentially destabilizing consequence for Egyptian leadership. Egyptian military tied government is taking the country on a path towards very gradual secularization and controlled democratization. It is copying Turkey's development and aspects of Putin's managed democracy. Egypt has not been an imperial ethnic core like Turkey or Russia however and is thus less stable since it's still a very young country. The popular dissatisfaction with the pace of progress among elites can trigger a transformative revolution.
Obama's speech made a historical gesture of mentioning CIA's coup in Iran but other than that, the tone concerning Iran was relatively cold. Iran's next presidential election will be hotly contested considering the incredible drop in the price of oil and corresponding drop in political patronage. The political infighting in Iran can be exploited against the backdrop of Arab liberals becoming more vocal. A more destabilized Middle East with Muslim extremists, liberals, and authoritarian governments all being centers of force, makes US economy a safer place to invest and for wealthier Arabs to migrate to and study in. A socially stirred Middle East is congruent with Obama's domestic economic restructuring since it can bring additional skilled workers into US, bring more capital, and allow US to begin saving money by withdrawing financial/military support from the region. Obama's speech in Cairo University hints at him being an incredibly cold blooded and pragmatic economic nationalist. Middle Easterners are yet to learn just how disinterested US has become in wasting resources in the region. Obama will try to save billions of dollars and save face internationally at the same time.