It’s simply focused kinetic energy that does it. The cone focuses the copper into a slug like object, and the slug becomes similar to an extremely powerful bullet.
The flimsy straw could do it simply because of how fast it was moving. The strength of the straw doesn't matter, simply it's mass, moving that fast, carries itself through, ie the leading edge is not being pushed from behind like a nail, more like a bullet with a string attached?
Setting aside the simplification, that probably the mass of the rest of the straw does play some part not absolutely zero, is that a reasonable way to conceptualize it?
According to this article, the National Oceanic and Atmospheric Association thinks it's not possible:
https://www.livescience.com/39270-tornado-straw-into-tree-wo...
(Alternative explanation in the article: the tree twists during the hurricane, cracks temporarily open, and debris gets stuck in the cracks.)