@Sh4dey I believe Mami's way of thinking is not simply about "If I can't be happily dating, Neither can you" or "I won't allow you to be happy before me" since her revenge doesn't necessarily revolve around her own happiness but more about taking it away from someone, in this case, MC. I'll explain in a bit about that, but first, we need to remember some things. We need to start on the bar episodes, in these chapters, Mami pretty much badmouthed the MC in front of their mutual friends and only once said something about Chizuru, which ended with Kazuya defending her but not himself. From there it all proceeds to the one on one talk about them getting together. We will come back to this later, now unto the beach arc is one if not the first instance where we see a glimpse of the real personality of Mami, why I say that is because, in this scene (the first ep of the beach arc, I think) we see Mami alone and posting online, in said messages she questions whether her ex-BF is trying to get back at her by getting a new GF so quickly, then proceeds to misremember Chizuru's name, following it up with her writing that the MC sided with Chizuru and finally stating she will make sure they break up (insecurities and revenge developing). From this point onwards, I will explain her way of thinking of "you can't be happy".
Mami, in the beginning, is not just seeking revenge against the MC, but she is also trying to restore her own image as the perfect girl, and it all comes down to the bar episode where her own sense of insecurity comes to the surface and preys on the MC and Chizuru by badmouthing them, here we can see her purpose, not necessarily to humiliate the MC but to salvage herself as an end result. This is further touched upon with her actions of wanting to get back together (probably to dump him immediately after), and later to dismiss and ignore the MC, those were the ways she was using to solve her insecurities and to take it out on MC and Chizuru. Hereupon, her quest for taking the MC's happiness away obviates restoring her own public image and threads to satiate her insecurities through means of revenge. The last bit explains why her own happiness doesn't matter in the revenge plot since it is also confirmed when we don't hear or see her dating anyone but instead, she is stalking, bidding her time and "planning" against the main characters. Finally, her pettiness and want for revenge comes down to the point of prodding both Kazuya and Chizuru about their relationship and taking joy of having learned their secret and knowing she could take them down anytime, that's why she plays and seems happy on the date with Chizuru and angry when she sees a purse on Kazuya's apartment after not finding him, she probably expected him to be grovelling and depressed after leaving them alone days later from the date with Chizuru.