Obama doesn't "sympathize" with the terrorist, but he is rhetorically soft on those Muslims that do.
I recognize that Obama "grew up Muslim" to a point; he was raised in an Islamic culture while in Indonesia, and he has Muslim family and friends. I don't believe he is a Muslim. I believe he's a loosely affiliated ecumenical Christian (who needs some serious time in Sunday School, IMO). I do believe that he has some personal issue with calling out Radical Islamic Jihadist Terrorists by name. Why this is the case is baffling. Perhaps there is some strategic aspect to it. More than likely, I believe that he does not want to offend Muslims, and, specifically, Muslims around the world that he may be acquainted with personally. I can understand this to a point. I do believe, however, that such considerations are secondary to reassuring Americans that he really is on their side. It's not fair that there is this alternative universe where folks choose their facts as well as their opinions, but it's a condition of the time. Obama's response to the times ought to be to reassure Americans who doubt before avoiding offending foreigners.
FB, it is much much more a point, which he has made clear many times, of not making this a "War against Islam" and thus making anti-Americanism a greater recruitment tool for ISIS. It's hardly accurate to associate Islam with ISIS anymore than it would be to associate Christianity with the KKK.
The "Radical Islamic Terrorism" catchphrase may play well to the American electorate as meaning "We mean only "radical terrorists" and of course realize that not many/most/all Muslims (depending on which Republican is saying it) support such atrocities." However, the vast majority of the Muslim world wouldn't hear the nuance vs. an attack on Islam in general.
And let's be frank: Whether taking quotes from FB's church members, the posts of many on this board, and the unfiltered thoughts of many politicians like Trump caught on camera demonstrate in their minds this really IS to large degree a war on what they view as a false religion.
