The reason the male lead can't easily discard the cousin is because the cousin playing a cliché character role that is super common in Chinese online fiction: the "white moonlight" love rival, aka the male lead's old flame that still has a hold on him because he couldn't stay with them, and thus became unable to forget them, over-idealizing them. In Chinese novels, any male lead that has a "white moonlight baggage" in his past usually needs to get over it first, along with his unrealistic, excessive idealization of the white moonlight, in order to start prioritizing the relationship he has with the mc. Think of the typical "white moonlight" character as the still-alive, Chinese variant of the Lost Lenore ( https://tvtropes.org/pmwiki/pmwiki.php/Main/TheLostLenore) in which the Lenore is still alive and playing a love rival role because "distance made the (male head's) heart grow (obsessively) fonder"...
Here's more info on the "white moonlight" character-type:
http://www.szdaily.com/content/2018-09/13/content_21080632.htm

Cousin needs to just leave... They didn't get together before and they aren't ging to now, so why in the hell does he have to be a winy little shit..... And Lin(?) needs to use his brain and realize hes in love with his best friend and do something about it and tell his cousin to f-off.