# Why would a molecule such as methane not dissolve well into water?

Well, methane is a non-polar molecule. These nonpolar molecules don't dissolve so well in water. You may have heard $\text{like dissolves like}$, since water is polar, it naturally tends to dissolve with other polar molecules.
Well, methane is a non-polar molecule that contains relatively non-polar $C - H$ bonds. The $C - H$ bond has negligible dipole moment, and even if it did have some polarity, the tetrahedral shape of the molecule would give no net dipole. Compare the solubility of ${\text{CCl}}_{4}$ in water which is also poor.
As chemists, as physical scientists, however, we should always seek out the data to inform our argument. This site quotes a solubility of $0.04 \cdot g \cdot k {g}^{-} 1 \text{(of water)}$, which is comparable to the solubility of the dinitrogen molecule under equivalent conditions.