Why do cephalochordates have no paired fins?

Cephalochordates, also known as lancelets, do not possess paired fins because they are primitive, fishlike marine invertebrates that lack the complex skeletal structures, such as a cranium or paired appendages, found in vertebrates.123

While vertebrates utilize fins and limbs for locomotion, cephalochordates rely on undulations of their segmented bodies to move through the water. Paired appendages are not present in ancestral vertebrates or modern cyclostomes, and they only appeared later during the evolution of fishes. According to the fin-fold theory, paired limbs are thought to have derived from the local persistence of parts of a continuous fold along the trunk of ancestral vertebrates; however, cephalochordates represent a distinct lineage that diverged before these complex appendicular structures evolved. Consequently, their body plan remains characterized by a persistent notochord and serial muscle segments (metameres) rather than the specialized skeletal girdles required to support paired fins.4512