If you try to translate from one language with a definite/indefinite article distinction to another (say English to German or Spanish), you'll notice that in many edge cases, one language uses a different article than the other (or one of them uses no article, while the other does).

The "I go to Church" example, is a case in point. In both German and Spanish, a definite article is required.

That shows that, while there is a systematic difference between "a" and "the", it breaks down in many edge cases.