Today's phrase comes from the literal rubbing of a cat. Apparently there is a way to do it and way not to do it. And when you do it the wrong way apparently you know. ( source ) Today we use it to indicate that someone has upset or irritated us...greatly. 

One theory to the phrase is military formation and the precise steps the soldiers are required to take. The steps start with the same foot for everyone, if someone starts off on the wrong foot the formation is tripped up - perhaps literally. The other theory is that if one gets out of bed in the morning with their left foot then they have started off the day on the wrong foot.  The different theories are explained here and here .  These days the phrase means anything that starts off badly - projects, relationships, etc - has gotten off on the wrong foot.