It's really best to take the high road in the admissions process and try to be as positive or neutral as possible about the school you're leaving. The new school usually knows what's going on anyway so the less you say the better. Rarely do admissions directors really push for reasons why you're leaving.
This advice describes our experience when we successfully applied out. Gave the forms to the teachers at the last possible date. I think they passed them to the Head as is the school policy. The new school understood the akwardness of the situation and didn't pry when we offered that we really felt that their school was simply a better fit. The old school didn't send the report cards as they said they had done and the new school's AD followed up with the old school on that. I kept all my communication focused on the new school and the subject never came up with the old school. The teachers never mentioned it and we waited until April when we found out DS was accepted from wait list. The old school Head never asked why we applied out.
The teachers were great about it. I know others who applied out and had negative experiences. I would avoid trying to justify your reasons with the current school - you aren't going to convince them and you don't need their approval.
Best of luck!