Transfer learning (TL) is a powerful tool for enhancing the performance of neural networks (NNs) in applications such as weather and climate prediction and turbulence modeling. TL enables models to generalize to out-of-distribution data with minimal data input. In this study, we employed a 9-layer convolutional NN to predict subgrid forcing in quasi-geostrophic systems and examined which metrics best describe its performance and generalizability. Fourier analysis of the NNs' kernels reveals that they learn low-pass, band-pass, and high-pass filters, regardless of their training dataset's isotropic or anisotropic nature. By analyzing the activation spectra, we also identified the reasons behind NNs' failure to generalize and how TL can overcome these limitations. The main reason is that learned weights and biases on one dataset underestimate the out-of-distribution sample spectra as they pass through NN, leading to an underestimation of output spectra. By only re-training one layer with new data from the target system, this underestimation is fixed and results in NN producing predictions matching target system dataset spectra. These findings are broadly applicable to data-driven parameterization of high-dimensional dynamical systems.