Exactly.  And very well said.  My Grandfather was a class-A old school bigot.  When IRA bombs went off he'd go on about the 'G.D. Irish" and the G.D. Catholics".  In his mind they were "all crazy".  When we see a statistically tiny number of people doing horrendous things it is absolutely wrong to hold the whole group responsible.  It also ignores the innumerable statements made by Muslims, easily found in five minutes of searching, condemning terrorism and violence.  It also ignores large protests in Pakistan and Egypt against extremism.
It allows the lunatics to control the narrative, which benefits them.  It helps the extremists in their efforts to radicalize disaffected people; they can point to headlines, newscasts, and comments by people who are essentially saying about Muslims what my Grandfather said about the Irish and Catholics.  So if you want lunatics to control what you think, jump on the bandwagon and help their cause by doing so.