Q. I was wondering, when I open my Tefilin bag, as all others I recall seeing, the zipper opens from right to left. The Tefilin Shel Rosh (head Tefilin) are placed on the right and since the Shel Yad (hand Tefilin), which we put on first are on the left side. Why is this not a case of 'Ein Maavirin Al Hamitzvos' (prohibited passing over the compliance of a mitzva) on the Shel Rosh, which appeared first?
A. Horav Shlomo Miller's Shlit'a opinion is that as long as the zipper does not open completely, it would be somehow difficult to extract the head Tefilin first and therefore they are not considered available at that time.
Only when the zipper opens completely they are readily available, and then the Shel Yad are closer.
In reality Tefilin bags that open from left to right are also common.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit'a