Well it is hard to say why he is doing that
Keep in mind I have only read your first post so if I reask I am sorry do not feel like reading through all the comments
I saw in the picture you drew that the red line is going straight towards to barrel I would say try going straight into the arena like you were headed to the third barrel then arch over into your frist barrel like your making the letter T for instance the pattern would look like this
Do you see what I mean by T?
But then agian it could be a number of things like his right lead could be hurting him, or the barn could be in the direction of the first barrel, or he could just be getting a little soar on the pattern. That last one is where a lot of people go wrong including myself.
I would run the pattern all day everyday if I could because I enjoy my horses on it but the best thing to do it just keep your horses in shap and supel. Best kind of practice is turning aunt beds in the pasture or evern trees or something round stay away from the barrels at home maybe only breeze the pattern at home once a month but other then that keep them on something new to them but the same thing to you so long as they can turn both directions the pattern should not matter