The main reason that I've heard so far is that it will touch the skin and bother your client. But as we all know we always have to use short lashes for inner corners, most commonly 5 mm and the most flat curl like B or C (depends on the brand). With such length and curl, lashes will never touch the skin.
Generally, it is quite difficult to work with the inner corners, since those lashes are thin and short, commonly fluffy, and have different directions. This is complicated to work with them, let alone setting a direction. And then you just need to get used to finding an individual approach, which side is better to attach a lash or a fan to in order to set the direction as you want, not following the direction of the natural lashes.
Surely, there are situations when you shouldn't direct lashes to the nose. For example, when your client has close-set eyes. In all other cases with this type of direction, you will visually lengthen the eye!
So, do not be afraid to direct eyelashes to a client's nose!