Qualitative understanding of variance formula

Hi,

      I don't quite get why: Var(U-V)= Var(U)+Var (V)-2Cov( U, V) . I get the covariance bit but why isn't it Var(U)-Var (V) ?

Student X

Understand that every variable introduced involves a certain amount of uncertainty (some may like to call it errors); the more variables, the greater the uncertainty. In this regard, separate variances of variables will reinforce each other as opposed to eliminating each other. Covariance is characterized as a quantity removed as uncertainty overlaps occur when one variable is somewhat dependent on the other.

Hope this clarifies. Peace.

Best Regards,

Mr Koh