Board Thread:General Discussion/@comment-28189972-20161129172223/@comment-26397825-20161129231041

It's more enemies that cause emotional and mental stress than fear, and force the Schnee to push past what they were and become stronger. From the transcript of Lessons Learned:

Winter : Excellent form! Now think to your fallen foes! The ones who forced you to push past where you were, and become who you are now. ( as the glyph flickers in and out of existence and Weiss grimaces in concentration ) Think of them, and watch as they come to your side.

And the manga revealed that t he Knight was a final test from her father; if she didn't defeat it she would not be allowed to go to Beacon. She had to push herself to achieve her goals, and become stronger than she was before she fought it.

The reason why the Schnee Mansion has the Knight statues that are the same as her summon is because her summon was pretty much one of those knight statues that was then taken over by a Possession Type Grimm due to some experimentation by the SDC. When she defeated it, it became her summon.