Oil came mostly from plant matter, buried in the time of dinosaurs and prior and subjected to time and pressure. The biomass of plants exceeds the biomass of animals by as much as two orders of magnitude.
Phytoplankton does not belong to Plant kingdom and neither do Zooplankton to Animal kingdom. Some Zooplankton are animals, which is subbranch of Eukariota to which most zooplankton belongs. Some of phytoplankton, like cyanobacteria are not considered to belong to plant kingdom, also most of plankton are supergrouped together with plants where most of them are not plants, but also belong to Eukariota. TL;TR: Animals and Plants belong to Eukariota, to which belong all plankton - even if most of them does not belong neither to Plants nor Animals.