Having written a couple of posts on the difficulty of loving others when you don't love yourself (here and here), I wanted to turn my attention to the struggles faced by the other person in such relationships, and there are several, which I address below as if speaking to this other person. (If you consider yourself self-loathing, try to imagine that your partner is going through some of what I describe below.)
Note: Some of the points below are drawn or adapted from past posts on self-loathing and relationships, in which I mentioned but did not focus on the other person. Naturally, some of these points are mirror images of the self-loathing person's issues discussed earlier, though some are developed further or in different ways.
1. If your self-loathing partner finds something missing in him- or herself, he or she may rely on you to fill that gap. This may feel good at first—most people like to feel needed, after all—but if it is taken too far, it turns into excessive neediness or dependency, and may leave you feeling less appreciated for who you are, not just for what you can do for your self-loathing partner.
2. It can be difficult to communicate with your self-loathing partner if he or she insists on reading the worst into things you say, projecting their own feelings of inadequacy onto you. You may find yourself closely monitoring what you say to him or her, possibly even letting communication decline altogether as it grows more frustrating and seemingly pointless.
3. As a specific example of problematic communication, your self-loathing partner may not handle praise well, either rejecting it ("no, I'm not smart"), minimizing it ("I just had one good day, it won't happen again"), or diverting it elsewhere ("sure, but look how well you did"). You want to encourage this person, especially if it may help lessen his or her self-loathing, but it is hard to maintain it for long if your partner continues to reject your support.
4. Similarly, your self-loathing partner may reject help when he or she clearly needs it, perhaps because he or she does not feel worthy of your care and does not want to impose on you. (Oddly, this can coincide with neediness—the self-loathing person may strongly desire some things from you while rejecting others.) It is extremely difficult to see the person you care about suffering, and it is even worse when you try to help but you are rejected, especially when you strongly believe that you can help if he or she would only let you.
5. The previous point, again, is an example of a more general problem regarding care: it can be very disheartening to care for someone who does not care for him- or herself. After a while, you can start to feel that your caring efforts are wasted; you spend time and energy trying to boost this person up, and he or she tries just as hard to tear him- or herself down again. (As an aside to the self-loathing person, the last point may be a core issue with loving others—or, more precisely, being loved—when you don't love yourself. It may be very difficult for someone else to love you if that person can see that you don't love yourself, in which case he or she may pour their heart into the relationship for naught.)
So what is the partner of a self-loathing person to do? If you have been with him or her for a while, you are probably a very caring and patient person—which is wonderful, of course—but you have to be conscious of your own well-being as well. You may derive immense satisfaction and fulfillment from helping your partner, in addition to the love and joy that he or she gives back to you, and the relationship may be worthwhile overall. If you can honestly regard his or her self-loathing as just a quirk that you can deal with at little cost to yourself, that's fantastic.
But if you find you are sacrificing too much of your own well-being in service to your partner's needs, if you're frustrated from feeling that your caring efforts are wasted, if you feel that your own needs are being neglected or suppressed, then something needs to change, whether that involves starting a dialogue about your concerns, or simply leaving. Whatever you do, please don't let your partner's needs eclipse your own—however much you care for this person, you aren't responsible for him or her.
Don't let other people's failure to love themselves make you forget to love yourself.