"That's the crux of the matter".
An expression we use when we have found out something that was not obvious at first.
But why poodle and why kernel? The idiom has its origins in the tragedy "Faust", the most important work of German literature.
What was it about? The scientist Dr. Heinrich Faust, unable to enjoy life and striving for more knowledge, meets a poodle on a walk, which behaves strangely and pursues him. Later, the poodle transforms into the devil Mephisto. The astonished Dr. Faust recognises "the core of the poodle". Incidentally, the "Gretchen question", a standing expression in the German language, also has its origins in Goethe's Faust.