One reason why the omitted variable leads to biased estimates is that omitting a relevant variable violates assumption 3 of the necessary assumptions of the classical regression model that states that all explanatory variables must be exogenous, i.e.

From this post, we know that omitting a relevant variable from the regression causes the error term and the explanatory variables to be correlated.

Continue reading Omitted Variable Bias: Violation of CLRM–Assumption 3: Explanatory Variables must be exogenous