Why non-controlling interest is added to equity

it doesn’t make sense at all. You don’t own it but add it to your book.

when you have control over a subsidiary, you need to consolidate 100% even though u only owned 80%

Asset is a Debit entry. When you consolidate (Debit 100% of) your subsidiary asset, you need to reduce the 20% somewhere with an opposite entry (Credit).

Equity is a Credit entry, so, NCI goes there.