Two-way breadcrumbs are great because some users want to remove a selection but with a one-way breadcrumb, everything past that selection disappears. However, with two-way breadcrumbs, it's impossible to change the selections at times. An example:
A dropdown with Fall, Spring, and Summer options, where we selected Fall.
We then select a college, and maybe gender.
I then remove college and gender and then want to go back and select Spring. I can't. I can only see Fall. I assume because the data is not for the fall so there is no way to go back and select Spring.