An intense-field theory of high harmonic generation from freely rotating molecules is developed. Explicit expressions of the high harmonic operator that govern the dynamic signal are derived and applied to analyze the recently measured dynamic (delay-time dependent) signals observed with the linear symmetric-top molecules. Results are given both for the usual experimental geometry in which the pump and probe polarizations are kept parallel to each other, and as a function of the relative angle between the two polarizations. They are discussed with special reference to the empirical fit formulas used earlier. Calculations are performed with respect to recent experiments and the results are obtained both in the time domain and in the spectral domain. Comparisons of the experimental data and the calculated results are made, and the role of the earlier empirical fits are partially justified. Finally, the origin of a number of hitherto unexplained salient features of the observations in the time and spectral domains is interpreted consistently by the theory.