Not sure if this is really a serious question, but here goes a serious answer.
The 1/2 rho v squared is essentially the kinetic energy density or kinetic energy per unit volume. Think of rho as mass over volume and the formula can be made to look like 1/2 mass v squared over volume. Of course 1/2 m v squared is the kinetic energy formula you would have learned during basic physics.
So where does the 1/2 come from in 1/2 m v^2? Try a simple derivation for an arbitrary mass that is initially at rest. If you move the mass over a distance, x, using a force, F. Then the work you perform is W=Fx. Substitute F=ma and recognize that without friction all the work you do increases the kinetic energy of the mass and you get KE=max. Now you assume constant acceleration over the whole distance and apply some basic calculus (or just borrow the answers from a textbook) and you kind that v^2=2ax, where v is the final velocity after moving distance x. Substitute back into the equation and you get KE = 1/2 m v^2.
It comes into the lift equation because that is developed using basic principles of physics. When the kinetic energy term (or more accurately KE density) is required a 1/2 shows up. It isn't associated specifically with the rho nor the v^2 but with the entire KE term.
A word of caution: with all physics you'll find that there are multiple ways of describing the same thing. It may be that you find a derivation where the 1/2 comes from somewhere else. That derivation may not be wrong, just different, but as long as the final answer is the same and the concepts are consistent then the alternate derivation is valid.