I feel like empathy was the wrong choice of word. Tolerance would have been a better choice.

Evil can abide good.
Good can not abide evil.

Evil is characterized by satisfying one's own desires at the expense of others. As an evil character you would not likely make any personal sacrifice - bodily, financially, or otherwise - to help a stranger without some sort of incentive, though you might stand by and watch your party help an innocent so long as their sacrifice came at no expense to you. You might scoff at them and tell them they're wasting their time on that worthless meat sack, but you wouldn't be obligated to stop them.

Good is characterized by self-sacrifice for the well-being of others. As a good character you would more likely put yourself in harm's way to mitigate the suffering of others. If you saw a couple of thugs roughing up a guy in the street to steal the loaf of bread he just bought from the bakery down the street, you could not reasonably sit by watching evil people doing evil things. After all, the only thing that's necessary for evil to win is for good to do nothing. As a good character you'd be obligated to jump in and help him, while your evil traveling companion scoffs and tells you that you're wasting your time on that worthless meat sack.

Evil is inherently self-centered, and the fact that each character has his own goals and desires gives the alignment itself the potential to have very personal implications for individual characters. They may want fame, or wealth, or power, or maybe they just enjoy the suffering of others. Depending on how the situation reflects on the character in question, evil typically has the luxury of using the "What you're doing doesn't hinder me in the pursuit of my goals, so I'm fine with it" excuse. An evil character should be willing to harm others in order to achieve his goals, but he doesn't necessarily have to go out of his way to harm others in circumstances where doing so would not be beneficial to him in some way.

Good is inherently self-sacrificing. Good doesn't care about a particular character's personal ambitions. Their ultimate goal is the same - if someone is in need, good is compelled to help. Good doesn't have the luxury of being able to pick and choose when it's appropriate to be good in the way that evil is able to bide its time for the opportune moment to strike. When an evil character performs an evil act he's generally choosing to perform that act, whereas when a good character performs a good act it's because he's being called to perform that act. Ignoring the call of someone in need means turning your back on your good alignment. The inward-focused nature of evil and the outward-focused nature of good are why evil characters can generally be more flexible in their actions than good characters without jeopardizing their alignment.