Mesons are indeed composite particles made up of a quark and an antiquark. Quarks are elementary particles that are classified as fermions due to their half-integer spin, which follows the Pauli exclusion principle. Fermions have the property that two identical fermions cannot occupy the same quantum state simultaneously.
However, when quarks combine to form a meson, the overall quantum mechanical behavior of the composite system is determined by the rules of particle physics and the properties of the constituents. The combination of a quark and an antiquark results in a bound state that behaves as a single particle, known as a meson.
The classification of particles as either bosons or fermions is based on their intrinsic spin. Bosons have integer spins (0, 1, 2, etc.), while fermions have half-integer spins (1/2, 3/2, 5/2, etc.). The composite nature of mesons does not change the intrinsic spin of the quark-antiquark pair, which remains an integer spin. Consequently, mesons are classified as bosons.
It's important to note that the classification of particles as bosons or fermions is based on their collective behavior and quantum statistics, rather than the properties of their constituents. Even though quarks are fermions individually, when they combine in specific configurations, the resulting composite particle can exhibit different properties and behavior, leading to its classification as a boson.