It's something I was always taught too and I keep to the tradition. Same way with handshakes - to shake with your left shows true friendship as it shows that you've laid down your shield (or secondary dagger in some circles) and truly trust the person. Similarly there's the custom of handing back a knife handle first so that you get cut not the recipient - a sign of trust. Also an old saying of stirring liquids or powders with a knife is often considered unlucky. One rhyme says, "Stir with a knife, stir up strife".
They do say that in chivalric circles it was considered bad form to shake hands with the same person more than once as as you had shown your trust you didn't need to show it again.
