I believe the correct word would be misanthrope or misanthropist.
As @theUg suggests, I am elaborating my explanation. Following are the reasons why I believe misanthrope should be the correct word here:
Misanthropy is the general hatred, mistrust or disdain of the human species or human nature. A misanthrope, or misanthropist is someone who holds such view or feeling. The word's origin is from Greek words μῖσος (misos, "hatred") and ἄνθρωπος (anthrōpos, "man, human").
- Scrooge as @JAM suggests could also be considered correct but not 100%, because the dictionary defines it as a person who is miserly. Also misanthrope looks much more formal. Same is the case with words suggested by others as they are not 100% correct for this situation.
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.
Best Answer
One could form a neologism "misindicist" or "misindist". Technically, "-phobe" refers to one who fears (not hates) something; "mis-" refers to hatred (not fear) of something. This would be formed on the analogy of "misogynist" or "misanthrope".