A Large Detector

The detector is so big for two main reasons, both coming from the need to measure particle momenta and energies precisely.

In the central tracking detectors, we measure the momentum of charged particles by how much the particle paths bend in the central magnetic field. For the highest energy particles produced at LEP1 the total bending over the 2m radius of the jet chamber is only about 2.6 cm. We need to measure this distance well to measure the particle momentum well.
When a hadron interacts in the detector, the typical length of the resulting shower depends on energy, and the density of the material. We can measure the energy of a hadron properly only if we detect most of the shower. We use dense materials in the calorimeters (lead-glass, iron) but even so the highest energy showers need about a metre depth of material to completely absorb them.