I think there are well-intentioned white folks who say All Lives Matter because they are trying to communicate that black lives and other POC lives should all be treated just as well as white lives. I don't think they appreciated the importance of saying Black Lives Matter and how All Lives Matter would be received by POC. Much of this was due to ignorance and a layer of subtle racism that most white people don't ever examine. This group is growing smaller as BLM is discussed more. I probably would have said All Lives Matter if I were speaking publicly about Ferguson and BLM in those early days.
These folks are generally educable such as:
Hillary Clinton: http://www.npr.org/sections/itsallpolitics/2015/06/24/417112956/hillary-clintons-three-word-gaffe-all-lives-matter
Martin O'Malley - http://www.cnn.com/2015/07/18/politics/martin-omalley-all-lives-matter/
Pres. of Smith College - http://www.washingtontimes.com/news/2014/dec/9/smith-college-president-apologizes-for-email-sayin/
And then there are the noneducable folks (at least in the short term) who are using it as a retaliation to Black Lives Matter. When they hear explanations about the importance of saying Black Lives Matter, they remain resistant or even get angry. Some are purposefully being antagonistic.
My family was the type that found overt, discriminatory racism offensive, but supported the less obvious types such as choosing to not live near Black people. We lived in a small (6000 pop) NYC bedroom community of mostly upper middle class, professional class, white people. To this day, there is less than 1% African American living in the community. It was much like and nearby where Corey Booker grew up. We participated in high school track meets together. There were fewer Black folk 30-40 years ago.