Terahertz (THz) communication is capable of providing ultra-wide bandwidth and high data rates. Therefore attracts widespread attention to its applications in next-generation networks. Highly directional antennas are used to compensate for the THz propagation loss, which also incurs beam management challenges. Specifically, caused by node mobility and blockage, frequent beam reselections and beam misalignment greatly degrade THz network performance in terms of reliability and spatial throughput. In this paper, using stochastic geometry, we fill the current research gap in system-level theoretical models for the analysis of beam misalignment and network spatial throughput by considering the effects of beamwidth, mobility, blockage, and molecular absorption. Our analyses show that an increase in nodes density or user mobility often results in severe beam misalignment, which in turn requires more signaling overhead and degrades THz network reliability and throughput. Although using wider beams reduces this impact, it increases THz network sensitivity to molecular absorption. To maximize spatial throughput, optimal beamwidth needs to be adjusted according to communication demand priority and network status. Our work provides useful insights into beamwidth adaptation according to parameters trade-off that helps THz network achieve higher reliability and throughput in different applications.