I'm not a fan of BEM either. It terribly feels like over-engineering and ignores certain principles of CSS. Often, much better clarity could be achieved simply with better naming and structuring of elements.
It's actually under-engineering (a brute force, hacky solution), and it ignores those principles of CSS (cascading for one) on purpose because they have been historically found to be more harm than good.
var the_first_left_menu_item_animation_enter
var the_second_left_menu_item_animation_enter
What causes this problem? Does CSS not have any modular capability and that is why? Is it global by definition? Not really sure what I am trying to say.
It has crappy scoping and modularity rules.
I'm always interested in seeing examples of good class naming and structure if you have some available.
BEM is more about specificity, modularity, and namespacing than it is about clarity (which many think it also achieves).