Imagine you are the proposer. You will start at the top of your list and work your way down only if rejected. So you are guaranteed to the best you could possibly do.
Imagine
A ranks X,Y,Z in that order
B ranks Y,X,Z in that order
C ranks X,Y,Z
X, Y, Z rank A,B,C in that order.
A will propose to X and match.
B will propose to Y and match.
C will propose to X and get rejected.
C will propose to Y and get rejected.
C will propose to Z and match.
Y will never get a proposal from A. Z will never get a proposal from A or B.
Edit: I think I fixed it.
Imagine A ranks X,Y,Z in that order B ranks Y,X,Z in that order C ranks X,Y,Z
X, Y, Z rank A,B,C in that order.
A will propose to X and match. B will propose to Y and match. C will propose to X and get rejected. C will propose to Y and get rejected. C will propose to Z and match.
Y will never get a proposal from A. Z will never get a proposal from A or B.
Edit: I think I fixed it.