The "eye for an eye" was actual Jewish law, but it was being used to justify personal vengeance.  "Turning the other cheek" does not mean submitting to persecution, but letting an offense go to shame  the offender (notice God's sense of humor and irony).  This passage is taken out of context by non-Christians to make Christians look weak and by Christians to justify apathy.  Jesus in Matthew 6 was speaking to combat legalism and misreading of the Law.