I second the Bannerman recommendation.
As for why -- we can use Bannerman to break it down.
A sacrament must be instituted by Christ. Maybe, maybe not. That is the question at hand.
It must be a visible sign of a spiritual grace. Could it possibly signify washing from sin? If it does it means the disciples wash away each other's sins. This creates a massive theological problem for the message of the cross. It also means it overlaps with baptism, which either makes baptism ineffective or foot-washing redundant.
It must be a seal of the covenant of grace. Definitely not. There is no authority in this action. The whole point of the action is to show the humble nature of service under Christ. The disciples are equal to each other. There is no "headship," no way of manifesting the "representative principle." Widows wash the feet of the saints. Do we now have women in positions of authority to administer sacraments. Besides, baptism initiates in the covenant, and the Lord's supper confirms it. What is left for another ordinance to do?
It must be a means of grace, a channel through which God promises to confer grace to the believer. Again, definitely not. Where is the promise to strengthen the faith of believers? Where is the symbolism in the letters of the NT? There is no "footwashing" into Christ as there is "baptised into Christ." There is no "footwashing" body of Christ as the bread which we break is called the "communion of the body of Christ." And we still have the problem that the disciples do this to each other. It is quite possible to leave God out of it altogether. There is nothing to bring us to God, which would be very strange for an ordinance.