Why does EEVEE not have a displacement option? When I switch in to EEVEE there is no micro displacement in the options.

Why won't micro displacement work in EEVEE?
Because no one has coded it for Eevee yet. Eevee can't use any of Cycles' displacement system. For best performance at least, it would need a completely new displacement engine based around OpenGL tessellation shaders. No one has gotten around to writing this yet, so for now Eevee just applies displacement nodes as a bump map.