Again, Jesus returns to the theme that the family relationships we cherish so much can't take precedence over him. Maybe in times of tranquility families that "pray together stay together," but when persecution is at hand and the chips are down, Jesus says he will divide families, not keep them together. He never says that you should focus on the family. He says that you should focus on loving him first and taking up your cross and following after him, so that when family members fall away you won't get carried away with them.
"I did not come to bring peace, but a sword." Not the kind of sword that Peter used to lop off the ear of the high priest's servant, but a sword that divides the hearts of family members from each other. It is the natural outcome of loving Jesus more than your spouse or parent or child. Even if a close family member doesn't demand that you stop following Jesus, they might ask if you could stop going to church so often, or try to discourage you from heeding a call to the ministry, or scold you for talking about Jesus in front of non-Christian relatives. Family members expect you to put them first, but when Jesus comes in between the relationship that can be scary for them. They might accuse you of being a fanatic or of having joined a cult.
When you follow Jesus you are called out of his world to live for the world to come, and family relationships are a part of this world. I don't know how we got into thinking that God called us to come to him as a package with spouse and children and parents along. It's true that God does his saving and sanctifying work through family relationships, but when we come to him we always come alone, with only our own hearts, our own commitments, and our own individual love for him. I don't see any room for bargaining or pleading with Jesus about how you'll only follow him if somebody you love comes too. That attitude is not worthy of him. While you may not have to abandon family ties for him, you do have to be prepared if it comes to that. It is the nature of the commitment.
If it does come to that Jesus says, "He who has found his life shall lose it, and he who has lost his life for my sake shall find it." God operates according to the principle of recompense. Whatever you lose for his sake in this life, you will be abundantly repaid in the next. So if following Christ costs you nothing, what will God repay you when you get to heaven? If you hold onto everything you have in this life, what do you have to look forward to in the next? Human love, even family love, is weak and fickle compared to the love of Christ. If you give him up to hold onto those human relationships, you are not worthy of him. It means you have never understood who he is and what a treasure he is to have, and you will be rewarded accordingly.