Why does a current mirror have low input resistance?
The input of an ideal current mirror should look for the input circuit as a short, as it is connected in series. Otherwise it will load that circuit and affect the current.

The output of the ideal current mirror should be an ideal current source, which, as you correctly said, should have an infinite resistance (it can be seen in the case of mirroring 0A current. In this case the output will effectively represent a disconnect).