Learn English – Person who suffers from unrequited love

Bigot or prejudiced come to mind. Bigot is a much more negative term, but even prejudiced has mostly negative connotations.

You’re asking a lot for one word.

The only reason that narcissist works as a single word is because of its extended use as a metaphor derived from classical mythology. In particular, it’s a direct reference to the myth of Narcissus, the boy who loved himself too much and others too little.

Unless you can find a figure from literature or myth to serve as a foil for both those properties at once, you’re going to have a hard time satisfying your request. And I can’t think of any.

The closest word I can find for someone who beats themself up too much, or doesn't have enough self-love, is a flagellant. But even that word is improved by an explicit self reference, as in an autoflagellant.

These aren’t common words, and you may risk being misunderstood. They might even get the wrong connotation altogether, such as being a masochist or religious penitent.

Trying to describe someone who hates themself with a single word is going to be hard, although I see why you would like one for this particular instance. Being too much the altruist or having a messiah complex won’t fit the parallelism of your phrase.