Obama's reaction is playing into political gamesmanship too. Actually, letting Trump's badgering get to him was a mistake.
There is an old saying: First one to lose his cool in an argument loses. Obama got played -- have to give Trump credit for getting away with that. Making a non-issue a point of contention
Terrorists are terrorists regardless of their religion or ideology. What is the difference between the IRA Catholic terrorist and the ISIS Islamic terrorist, or for that matter the Nazi terrorist SS v. today's ideological terrorist -- not a fucking thing ...