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Subtitles in anime are someone's adaptation. If you give a show to three different translators, you'll get three different sets of subtitles. What you're reading, is in fact, not the original.
Subtitles are limited to how many characters can fit on screen, so sometimes the full translation has to be shortened to fit that character limit, meaning information may be missing. Translators also have to make Japanese sayings or jokes work in English.
This means their translation is often different than the original joke, because the joke may stem from a pun that wouldn't make any sense in English. As adaptive writers, we have to take the translation, which is already an adaptation, and adapt it further to fit mouth movements.
The moral of this story is that unless you speak fluent Japanese, whether you watch subs or dubs (Both are fine!) you are watching someone's adaptation, and it will always be different than the original. Translators and adaptive writers are all doing their best. 
