Things that feel counter intuitive (I'm sure there are more ...) -
1a) For swords with edges, holding your blade closer to you is safer than holding it away from you (distance varies depending on single or 2 handed weapon).
1b) If cornered and panicked, it's safer to pull your sword towards your center than slash about away from your body.
2) Looking at an incoming cut is safer than turning your head away from it.
3) From contact, it's often safer to close on your opponent than back out again.
4) You can reach further if you drop lower.
5) Letting go the weapon is sometimes safer than trying to keep hold of it.
6a) You can gain advantage by slowing down.
6b) Stealing the timing by slowing down or stopping can be just as effective as speeding up.
7) One of the most dangerous moments for you is when you are striking.