"2=1"
Let X=Y
X^2=XY
X^2+X^2-2XY=XY+X^2-2XY
2(X^2-XY)=X^2-XY
2=1

The flaw:
You multiplied by 2 on one side...
1 = 1
1^2 = 1*1
1+1-2=1+1-2
2 - where does this come from? (1-1)= 1-1
0=0

second proof:
3 = 3
3^2 = 3*3
9+9-9=9+9-9 - if you multiply by 2 on one side you have to on the other, or else you've changed the equation. It works for 1 because 1 is the only number which is its own square.
2(9+9-9)= 2(9+9-9)
18=18

Big whoop.

Did I miss anything?

Thanks for nothing...

-Marcel