# Why does Lasso Regression shrink coefficients to 0 instead of uniformly decreasing all coefficients [duplicate]

Lasso regression uses an L1 penalty which sums the absolute values of all coefficients. In this answer, the responder gives a scenario where we can either select 10 and 0 for coefficients, or 5 and 5 and get the same penalty. Lasso regression is known for feature selection (i.e. zero'ing out coefficients), but Why / How does Lasso regression do this instead of just decreasing all parameters?