Cubs usually don't have a lot (if any) wing Dihedral which is where an Airplanes "self righting" characteristics come from. All High wing airplanes are not created equal. Cubs usually aren't recommended as first planes because of that reason. The exception is the little SuperCub foamy, but it has no Aileron control unless you modify it yourself and add some. It has to be flown on calm wind days tho or you'll be fighting the wind, its pretty nifty the first time you see it flying backwards tho.

Edit: Some Cubs are modified by the manufacturers to include some Dihedral to make them more beginner friendly.