I saw this meme, and another similar to it that I will address in another post, while searching for an image for a blog post. This deserves an answer, so I will attempt to answer it.
When resolving supposed condratictions in Scripture, there are several things you must take into consideration.
1. Who is the audience?
2. Who is the speaker?
3. What is the context of the surrounding passage?
4. Are there varying meanings for the same word depending on how it is used?
5. Is the version of the Bible in question a reliable translation? The Good News Bible, The Message and other paraphrases are not reliable. The KJV, NKJV, NASB, ESV are some of my favorites that are from reliable sources.
Let's look at the Luke 14:26 passage first.
“If anyone comes to me and does not hate his own father and mother and wife and children and brothers and sisters, yes, and even his own life, he cannot be my disciple. Whoever does not bear his own cross and come after me cannot be my disciple. For which of you, desiring to build a tower, does not first sit down and count the cost, whether he has enough to complete it? Otherwise, when he has laid a foundation and is not able to finish, all who see it begin to mock him, saying, ‘This man began to build and was not able to finish.’ Or what king, going out to encounter another king in war, will not sit down first and deliberate whether he is able with ten thousand to meet him who comes against him with twenty thousand? And if not, while the other is yet a great way off, he sends a delegation and asks for terms of peace. So therefore, any one of you who does not renounce all that he has cannot be my disciple. (Luke 14:26-33 ESV)
Jesus is the speaker and the audience are the crowds that had begun to follow Him around. Jesus wants them to know what it may cost them if they continue to follow Him. Soon, it would not be popular to follow Him and those who chose to do so would risk being put out of the synagogue, even disowned by their parents and siblings. Even today in many Jewish families, if a family member converts to Christianity and follows Jesus, they are disowned by their family and even considered dead as far as they are concerned. So for Jesus to say "“If anyone comes to me and does not hate his own father and mother and wife and children and brothers and sisters, yes, and even his own life, he cannot be my disciple", meant that you could not love your family above Him, because if you did you couldn't be His disciple. You had to be willing to be disowned by your family and even put to death by those who hated Jesus if you wanted to follow Him. If you followed Jesus, your family would take it that you hated them. You had to love Jesus more than you loved your family, because you would most likely lose your family if you followed Him. This is what is meant by hating your mother, wife, children, brothers and sisters.
This "hate" is not the vindictive, murderous hate that is talked about in 1 John 3:15, where it says, "Everyone who hates his brother is a murderer, and you know that no murderer has eternal life abiding in him." Jesus explains why vindictive hate is equal to murder.
And he said, “What comes out of a person is what defiles him. For from within, out of the heart of man, come evil thoughts, sexual immorality, theft, murder, adultery, coveting, wickedness, deceit, sensuality, envy, slander, pride, foolishness. All these evil things come from within, and they defile a person.” (Mark 7:20-23 ESV)
It is a heart issue. When you hate someone, in effect you are wishing they were dead and therefore you have murdered them in your heart. This is vastly different from the "hate" talked about in Luke 14:26. They are no where the same, so this meme was apparently written by someone who doesn't understand the teachings of Jesus or the culture in which He lived.