We investigate the ionization mechanisms for hidden broad-line region (HBLR) and non-HBLR Seyfert 2 galaxies by comparing some optical emission line ratios. We note that the [N II] λ6583/Hα ratio of the non-HBLR Seyfert 2 galaxies is significantly higher than that of the HBLR Seyfert 2 galaxies while other line ratios, such as [O III]/Hβ and [O I]/Hα, are similar. To probe the origin of this difference, we explore theoretical results of different ionization models, such as photoionization, starburst, and shock models. We find that none of these models can explain the high [N II] λ6583/Hα ratio of the non-HBLR Seyfert 2 galaxies with solar abundance; the high [N II] λ6583/Hα must be reproduced from enhanced nitrogen abundance. Since nitrogen overabundance can be achieved from the dredge-up of red supergiants in the post-main-sequence stage, we suggest that the observed nitrogen overabundance of the non-HBLR Seyfert 2 galaxies might be caused by stellar evolution, and there could be an evolutionary connection between the HBLR and non-HBLR Seyfert 2 galaxies.