Like in Tonari no Kaibutsu-kun, the female lead has inferiority complex towards the male lead for being a genius. Or in Kare Kano, the guy thinks that he and female lead are similarly 'fake' at first, but then she comes out of her shell and becomes her own person while he can't do the same thus he thinks she's 'abandoning' him, and in some way he generates a complex toward her. They do love their partner but can't help the growing ill-feelings that consume them. Like love-hate relationship, except it's not end with simply bickering, but as an actual threat to their relationship, real 'hate'.

As usual no BL, everything else is fine. Thanks in advance

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DONDAKEE!!

Last Game - Yanagi (male lead) can not beat Kujou (female lead) in anything. So he hates her, but also is madly in love with her.

Special A
Not sure if it qualifies as "complex towards lover" but they are always trying to beat each other in academics.