The problem with the subjective is that it barely exists in modern-day English. "I believe that he see the difference" just is not proper English. There are a few cases of English grammatical structure reflecting the subjective -- for example, I could say, "It makes me angry that you should say that," -- but in general, that sounds very old-fashioned. You'd be more likely to hear a native English speaker say, "It makes me angry when you say that," or something to that effect. In other words, indicative is everywhere.
I don't know what your native language is, but if it's a language other than English, it probably feels instinctively wrong to use indicative in English when you "should" be using the subjunctive, but that's just the way it's done.
However, you can have the last laugh, since it's incredibly difficult for English speakers to understand the concept of subjunctive, much less know when and how to properly use it! So you have a big leg up in that regard.
I know that people seem to think that the subjunctive is difficult for English speakers, but I haven't had too much trouble with it. What I think is interesting is the difference between its use in Spanish and Italian, in the sense that I don't think it needs to be used with positive thoughts and beliefs in Spanish, but does in Italian.
The Italians or Spanish when speaking correctly would always use the subjunctive here. Ordinary people speaking naturally in Spain (Italy?) will use the imperfect subjunctive too (good luck with that!) However in normal English, wherever it is spoken, the translation would either be using the indicative as here or if one wishes to stress the uncertainty we would insert might / could / would or even should / ought. Although English does not use the subjunctive apart from instants such as "if I WERE you", we can express subtle differences in meaning by using might etc.