If there is such a thing as "weak Hadith," why were they included anyway?

I guess the "science of Hadith" done by the Hadith collectors didn't use the same science for all of the Hadith? Some Hadith got some "science," while others got some other "science." Either your books are authentic, which means everything in them are authentic, or they aren't. Choose please. Stop confusing outsiders and even those inside your circle.