Why is there a dip in this Chebyshev filter response?
You are confused about which parameters are what.  The $S_{11}$ parameter is the power that's reflected back from the network; the $S_{21}$ parameter is the desirable bit that's passed forward.
Just by conservation of energy, if the filter is lossless then $\left | S_{11} \right | = 1 -  \left | S_{21} \right |$.  So that horrible deep null in $S_{11}$ actually just means that $S_{21}$ is at unity, which is desired.