After posting this question, I investigated why I don't understand the sound difference, and I found out that one of the reasons must be the different dialects that exist in the deck. I installed the sample English deck from this website, which says:
The sound files are from Forvo.com and they are in various dialects.
However, I now wonder if it is a good idea to mix the different dialects into the single deck and train my ears. Not only have I practically no experience on non-American dialects, but I cannot know which dialect it is after flipping the card. Thus, on the failed results I can't even know if it is my misunderstanding or the different dialect.
I have practically zero opportunity to talk with native English speakers and all people I have spoken and will speak with in English are non-native speakers, the vast majority of which don't even care about their pronunciation. I also have no plan to go to any English-speaking countries. I grew up with American accents as that is what is taught in school.
In this case, how should I compose my minimal pairs deck?