What's your pattern? Can you link to it? It may not matter a lot what cast on you use. If the pattern is lace then there may be a specific reason. If you need a stretchy cast on there is a version of the knitted cast on that is quite stretchy. In this video it's called The Lace Cast On
. It could be something to do with the appearance of the cast on. If stretch is the issue there are various long tail cast ons that are very stretchy. So the answer is: It depends.