I have just moved to back button focussing over the last 3 months.
I shoot sports almost exclusively. Continuous focus mode.
It still catches me out "in the heat of battle" ... I will instinctively hit the shutter release without having focused with the back button ... or I will press harder with the back button, without even touching the shutter release!!! I have taken the advice of others to keep at it. I am certainly getting more comfortable with it.
The single most compelling reason FOR ME to change was the realisation that back button focussing allows for TWO modes of focussing without having to change any settings.
1) AF-C: continuous focussing - just hold the back button down whilst you follow the action. (this is what I would do for 97.256% of my shooting
2) AF-S: single shot focussing - pick the subject element you want to focus on. Press the back button until it acquires focus, then RELEASE ... recompose to suit.
Until I went to back button focussing, I could not do BOTH without having to change the focus mode setting - often inconvenient or missed the shot.
That has been the ONLY advantage for ME in what I shoot - but it is a big enough advantage for me to stay with it. It is taking some time to develop the coordination to control two buttons in a shooting sequence rather than just the shutter release.
Two other issues for ME have also arisen.
1) because I shoot with my left eye, I have had to alter my positioning as I found my thumb was pressing too hard into my face!!!
2) on my gripped camera body, when I shoot in portrait orientation, I have a less secure grip on the right hand side of the camera body. Whereas before I had the right hand thumb to also grip firmly on the back of the camera, now I don't hold it so much with my right thumb and it feels less secure.
If anyone can provide some suggestions on that issue, I'd be very grateful.
Sometimes, when I'm shooting, I think I should maybe go back to using the shutter release ... BUT that soon gets dismissed when I think about (and use) the two separate modes of focussing WITHOUT having to change the setting on the side of the camera. In shoots that involve a mixture of static and moving subjects, it is a no brainer - back button is much more efficient and versatile.
I am getting more confident with it as I keep using it. As I said, in moments of really fast situations, it is not as intuitive for me as I would like ... but I'm going to stick with it. I know people have said once they started using back button focussing, they would never go back. I can see now why they say that ... I will certainly stick with it.