Why does Nick admire Gatsby (in the Great Gatsby) despite and perhaps because of his faults?

because G-man throws the awesomest parties and gets all da bitches to come to his big-asss house. Gatsby is also loaded with green gold (millions of them) and wants to bang Nicks sexxxy cousin Daisy

Nick, similar to his creator Fitzgerald, is an aspirant to the upper-crust of society. But, unlike the phonies at Gatsby's parties, Nick knows he would retain this humanity even with success. In Gatsby he saw someone who was an innocent as the day he first laid eyes upon Daisy, forlorn though his love was, the emotion itself remained uncorrupted. This aspect of Gatsby was admired by Nick.

Because Gatsby is classy

because Nick is attracted to imperfection, clearly.