You can empathize without sympathizing.

It can't be easy. I would like to empathize, but I can't. All I can do is sympathize with him.

The other often much prefers a clear answer, even if it is No, than continued indecision and waffling.

You're the enemy. I don't want to sympathize with you. So... So don't... Don't cry like that in front of me! Damn it...

We sympathize, but that remains to be seen.

We know what they're going through. We sympathize with them, ... We're still Southerners and we're still pulling together. It's all sweet tea and casseroles.