not so, the Pharisees liked to add to the law making the traditions of man the commandments of God, such as handwashing. this is the same in this case, the Pharisees were adding to Gods law. Jesus cannot break any laws otherwise he's now a sinner, Jesus cannot sin. also, the Sabbath is a shadow of things to come, just like the animal sacrifices and dietary laws, these were all done away with in the new testament.
Jesus did not oppose exodus 21, how can he oppose himself? when he said that in exodus, it was for the government to follow out, not just us individuals, Jesus's main teaching there was to teach grace and mercy, if someone hits you, instead of taking revenge and hitting them back, just turn the other cheek. nowhere did he say the law was wrong, the law is not sin.
there's no contradictory advice, firstly you must be reading these modern versions that's why, i strongly recommend a KJV, secondly, you're simply misinterpreting and not fully studying the bible, many just read a verse here and a verse there and then say "contradiction!" without reading the context or comparing scripture with scripture as advised in Corinthians. my advice is to read the whole bible cover to cover to get the bigger picture, then you'll be able to see how everything goes hand in hand and isn't contadictory.
am i going to get that question answered?