Answer:
Say you don't have pets but a friend or acquaintance of yours does. Their pet dies. You think it's not that big of a deal because it's "just an animal" so you tell your friend that.
This would be a lack of empathy as you fail to realize the mental impact an "animal" could have had on that person. Also a lack of respect as you would have failed to acknowledge the persons opinion, not on purpose, but you would have. Making them feel less.
^ That one's a little harsh.
Say someone burnt a dish they had been working really hard on and they're distraught over it. You tell them it's just a dish and you can try again and to not be so hung over something so little. In this situation you would have failed to realize how much time and effort the person might have spent in that dish. The importance or excitement they may have felt all for it to not work out in the end.
Someone loses something they've had since they were a child, you tell them it's not important because it can't be used in the present. You would have disregarded how the person felt and the close attachment that item may have brought to them.