Why on manifold, we rather use Stratonovich integral rather than Itô integral?

Question

I start to stud stochastic calculus on manifold, and I see that on manifold, we rather use Stratonovich integral rather than Itô integral. Is there any reason for that ? Indeed, Stratonovich integral has not nice properties as being a martingale for example. So, I feel a bit strange to use it rather Itô. Any motivation known ?