I just don't understand why, if something doesn't work, consulting the help is not the first thing that everyone does. The MSDN doco for that property says:
Property Value
true if the list is an IBindingListView and supports filtering; otherwise, false.

Remarks
If the list is not an IBindingListView, SupportsFiltering always returns false.
Does the BindingList class implement the IBindingListView interface? The answer is NO. There are not many classes that do. BindingSource and DataView do, and I'm not aware of any others in the Framework, although there may be some. The fact that DataView does is the reason that you can bind and filter DataTables. If you want a list that supports filtering then you have to implement it yourself.