Solar filaments, also called solar prominences when appearing above the solar limb, are cold, dense materials suspended in the hot tenuous solar corona, consisting of numerous long, fibril-like threads. These threads are the key to disclosing the physics of solar filaments. Similar structures also exist in galaxy clusters. Besides their mysterious formation, filament threads are observed to move with alternating directions, which are called counterstreaming flows. However, the origin of these flows has not been clarified yet. Here we report that turbulent heating at the solar surface is the key, which randomly evaporates materials from the solar surface to the corona, naturally reproducing the formation and counterstreamings of the sparse threads in the solar corona. We further suggest that while the cold Hα counterstreamings are mainly due to longitudinal oscillations of the filament threads, there are million-kelvin counterstreamings in the corona between threads, which are alternating unidirectional flows.