I guess we've all encountered the many ways to deal with others' pain without empathizing.
There are people who jump to give advice that may not be suitable.
There are people who blame the victim.
There are those who utter condemnations.
There are those who ridicule or make light of the other's pain.
There are those who try to dismiss the other's pain with various platitudes, some generic – "Oh, that's just how people are." And some religious – "Oh, you just need to pray/trust in Hashem."
We all do this at times. Sometimes, someone expresses an emotion or reveals a situation that cuts too close for comfort. We may experience a similar emotion or situation with which we struggle. Since we haven't figured out how to deal with it in ourselves, a wall goes up within us when faced with it in others.
Yet if we truly understood that Hashem runs things, we wouldn't feel the need to deny the other's pain. In such situations, we often feel helpless or threatened. Yet if we truly knew that we could help the person through spiritual efforts – the most effective way to help another person – then we wouldn't feel helpless or threatened. This is why the most elevated people, like Rav Aryeh Levin, were able to sit and listen to people for so long and so often.
Perhaps people who consistently lack empathy remain unaware that they don't really believe in God as more than an impersonal Creator or perhaps they struggle with overwhelming pain and secretly take issue with the way God runs their life – no matter how pious they seem. With such apparent deficiencies in their own religiosity, their wonky responses need not be taken to heart.
Of course, this does not mean that you can't place boundaries on a distressing relationship. Part of acknowledging Hashem's involvement includes the understanding that you are not that person's savior – Hashem is.
You are not that person's only hope – Hashem is.
Despite our sincerest intentions, feeling overly responsible to "fix" another person can indicate a deficiency in our own emuna and belief in Hashem's omnipotence. If you see that you cannot help a person, or that a person is using you as a dumping ground for bitterness and/or lashon hara, then it is good, even mandatory to disconnect – while still davening for that person. In fact, spending half an hour praying for a suffering friend can actually help and improve her life much more than spending two hours "helping" her in person.
I'm not saying we shouldn't help others – of course we should! But if you see that your "help" does not actually help, it could be that Hashem is trying to get you to redirect your heartfelt efforts.
(And in case you're wondering...yes, I learned all this the hard way!)