I agree with Chris. As an example, “The library is the opposite of my home” might mean “My home is noisy but the library is quiet.”

The library IS opposite my home. Is the correct way. With your way, its as if you are comparing your home with the library in some way.

"The library is opposite my home" is usually the short version of "The library is on the opposite side of the road to my house." Swap 'road' for whatever is appropriate.. e.g. street, avenue, river, even city!