When creating an animation by code (add KeyFrame to AnimationClip then finally add AnimationClip to Animation and Play() ) if making a keyframe for "rotation" you will get a special keyframe that will have a sharp broken at the middle of 2 keyframes.

2) How can we reproduce it using the example you attached
Try this on a GameObject that has Animation component attached

AnimationClip dieAnimation = new AnimationClip();
AnimationCurve rotationCurve = new AnimationCurve();
rotationCurve.AddKey(new Keyframe(0.5f,0.3f,0,0));
rotationCurve.AddKey(new Keyframe(1,0,0,0));
dieAnimation.SetCurve("",typeof(Transform),"localRotation.z",rotationCurve);
animation.AddClip(dieAnimation,"dieAnimation");
animation.Play("dieAnimation");

At runtime check the newly created AnimationClip in the Animation Editor to see that the light-blue keyframe belongs to localRotation.z has a very weird shape. Try drag around for a weirder shape. (If the two are really close, the shape will be ok)