Short answer Because of tradition. In the Shvetambar Jain community, the public reading of the Kalpasutra is scheduled so that the Janma‑Vanchan (the “birth reading” of Bhagwan Mahavira) falls on Panchami, the 5th day of Paryushan. To make that happen smoothly, many sanghs start the serial reading on the 3rd day. This timing also lets the first two days be focused on pratikraman, taking vows, and settling into austerities; then the scripture‑reading begins with full attention from the 3rd day.

A little more detail

• Shvetambar practice: Kalpasutra is read during Paryushan. Different gacchas/upashrays follow slightly different schedules. Some begin on the 3rd day, others on the 4th; both are accepted in their respective traditions. The key is that the Janma‑Vanchan occurs on Panchami with full sajjā and reverence.
• Why not from day 1? The opening days emphasize inner preparation—aloyan (introspection), samayik, and firming up fasts/anuvratas. After that, the sangh gathers in larger numbers and listens to the Kalpasutra with steadier focus.
• Digambar note: Kalpasutra is a Shvetambar text. Digambar Jains observe Das‑Lakshan during the same period and typically study texts like Tattvartha‑sutra instead of Kalpasutra.

So, starting on the 3rd day is a respected paramparā meant to honor Janma‑Vanchan on the 5th day and to keep the spiritual flow of Paryushan intact.