Is Eve just desperate or just plain stupid? I really don't understand her logic in all this.
Now I can come here, since in my viewing (first time since orig. airing) Eve is clearly gone... you know, who knows? She could come back from anything on DS. But anyway, as for the question asked, it's perfectly sensible. People often wonder why an obviously unsensible character doesn't think or act sensibly. People are different, with different views of the world and motivations than ours.
It's the most common thing in the world for one person to be so in love with another, or so infatuated, or fixated, or whatever (latter two in Eve's case I'm sure) that the infatuation is so overwhelming and so keenly felt by the first person, that he or she cannot imagine that the other person does not share in it. This is experienced as something more solid than any logic. I think that some people probably think of love as something separate from themselves, that exists "out there", in the space between the two people, or in a space enveloping the two people*, or else it wouldn't feel so enormous and "real". What they feel is just inside themselves, though.
Besides, killers are selfish and self-obsessed. They decide things for other people... whether they get to live, whether they're in love, whatever. Not having the ability to call the shots doesn't occur to them. Reality is what they say or think it is.
*Perhaps Prof. Stokes has a theory about this "love bubble".... an alternate state of existence that can't actually happen in our continuum....