Why does Yale discriminate its applicants based on race?

It appears you do not understand and accept the American legal system. A defendant is considered innocent until proven guilty in a court of law. 

Courts have previously ruled that universities may consider race as part of their admittance policy to increase diversity, but may not have racial quotas.

An effort towards a more diverse college experience.  A very common consideration/practice in many universities.

Yale is a liberal school and liberals love their identity politics.    Such liberal schools are very influenced by the teachings of cultural Marxist philosophy which advocates people should either be advantaged or disadvantaged based on their race.   It essentially argues that races that do well must be oppressing those not doing well.  In the case of higher education that means Asians should be disadvantaged while other minority races such as blacks should be advantaged.   

It’s an argument that doesn’t hold up to scrutiny but that doesn’t matter.   Identity politics is now incredibly ingrained in liberal agenda.   

You need to be smart enough first -- be able to afford it ,second .

So what racial correlation with those are you making ?