We first clarify confusing terms for three unstable modes of the Parker instability in a perfectly conducting compressible plasma in the horizontal magnetic field and the vertical gravitational field. We call them as interchange, undular, and mixed modes following Matsumoto et al. (1993). We then provide three counter evidences for the notion that the Parker instability can form giant molecular clouds (GMCs): a short lifetime of the GMCs based on a recent turbulent picture, a stabilizing role played by the random component of the magnetic field, and a low degree of density enhancement brought by the instability. Instead, the instability may be responsible for corrugations in spiral arms.