I am not claiming my 20 year old income earning daughter as a dependent, why are full time students earning income from w-2 wages not allowed to apply for EITC?

If she is 20 and she is a full-time student ---she CAN be claimed as a dependent---so she is supposed to say on her own return that she can be claimed.   Dependents cannot get EIC --- or stimulus money.

https://ttlc.intuit.com/community/dependents/help/when-do-i-have-to-answer-yes-to-being-claimed-as-a-dependent/00/1994319

WHO CAN I CLAIM AS A DEPENDENT?

You can claim a child, relative, friend, or fiancé (etc.) as a dependent on your 2021 taxes as long as they meet the following requirements:

Qualifying child

• They're related to you.
• They aren't claimed as a dependent by someone else.
• They're a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They're under the age of 19 (or 24 for full-time students).
• No age limit for permanently and totally disabled children.
• They lived with you for more than half the year (exceptions apply).
• They didn't provide more than half of their own support for the year.

Qualifying relative

• They don't have to be related to you (despite the name).
• They aren't claimed as a dependent by someone else.
• They're a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They lived with you the entire year (exceptions apply).
• They made less than $4,300 in 2021.
• You provided more than half of their financial support

if she is supplying more than 1/2 of her support (unusual) then she can not be claimed as a dependent by you. and she should mark her return that she can not be claimed as a dependent. otherwise, she should indicate she's someone else's dependent and you should claim her as a dependent. 

https://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf