Here's the thing I don't get ...
At some point you are introduced to baseball, and you start to use stats. Let's say you start with average (you are new to baseball, good place to start). You notice a trend that the better players have averages over .300. But after time, you start to realize that not all .300 hitters bring equal value. There's a difference between the guy hitting 180 singles and the one crushing 40 home runs along with it. I mean, everyone must have that thought at some point.
Then, you start to expand. You might discover OBP or SLG. And now you are incorporating those stats. But then you start seeing things like, hey, that hitter on my team consistently steals 50 bases! So you might want to evaluate baserunning (man, he sure does take that extra base more often than the next guy). Or there's that guy that plays an amazing centerfield. So you start to look at some simple fielding stats.
In other words, you are just looking at various stats that try to place value on the things that you see. The "traditionalists" do this. Everyone does this. And they are all using stats. Now, this is where I don't get where the 'hate' comes in ... someone who might be using an advanced stat is only using that stat because they've asked all those questions and someone really smart put together a stat that tries to incorporate all the natural observations that you have had (e.g. not all 300 hitters are the same).
I just don't get what the big deal is. I think if you sat down with the Murray Chasse's of the world, and just had a normal conversation, and didn't even bring up the advanced stats, but just asked questions, they would realize that they agree a lot more with the 'geeks' then they think they do. Hey Murray, do you think all 300 hitters are the same? Do you think that defense and value brings value? etc.
This is such an odd/weird debate.