She can't justify or excuse this, because you're right: Christians are called to be kind and loving toward others. But constantly criticizing others isn't kind and loving - not at all. Jesus warned "that men will have to give account on the day of judgment for every careless word they have spoken" (Matthew 12:36).
Have you ever asked yourself why your aunt behaves the ways she does? One reason some people have a critical spirit, I've found, is because it makes them feel superior to others. Down inside, they feel insecure and inferior (even if they don't realize it) - and criticizing others is a way of overcoming that feeling. But it never works, because it does nothing to help them overcome that deep sense of worthlessness. It also makes others dislike them - which only increases the problem.
God doesn't want your aunt to be this way - both for her sake, and for the sake of the Gospel. Who knows what damage she has done to the cause of Christ by her harsh words? Pray for her, and ask God to help you confront her about this issue - not in anger, but out of love and concern.
Then make sure you don't fall into the same trap. Satan loves an inconsistent Christian - but when we stay close to Christ, God helps us overcome these things. Remember Jesus' words: "Let your light shine before men, that they may see your good deeds and praise your Father in heaven" (Matthew 5:16).