True love is the most powerful motivator. It reaches further and lasts longer than hate, power, fear, sex or wealth (some other motivators). But love itself presents a challenge; we will always behave in a way that pleases the person we love most. Jesus' statements in these verses highlight the challenge: do we love the Lord most of all, or our family?
 
Now, that is not to say that children should not honour and obey parents (Ephesians 6:1-3); provide for older parents (Mark 7:9-13; 1 Timothy 5:8); care for widows and orphans (James 1:27). That is all part of our Christian duty. Serving people in their needs is an essential mark of love. But to be deflected from serving the Lord because of anybody's demands is not right either (Acts 4:19). It all comes down to who we love most. Loving Christ and serving Him does not mean that we reject our family, but that we refuse to be manipulated by them away from our allegiance to Jesus.
 
That often involves much heart searching, loving service and distress if our family cannot or will not appreciate that our love for Jesus must come first. It is a personal sacrifice to live without the family understanding or approving: that is what Jesus means by 'take up their cross'. It may even risk our lives. But those who want to live their lives in the popularity and approval of others may find that they lose their eternal security; whereas those who live to please the Lord more than anybody else, will win His reward.
 
Practically, this can be a very difficult matter to get right; trying to please everybody may result in pleasing nobody, especially the Lord. Yes, we need to live peaceably wherever possible (Romans 12:18), but not to compromise the priority of pleasing the Lord. It is all a matter of who we love most, whose opinion is most important. Unwillingness to risk rejection for the sake of Christ describes the state of our faith; that we do not love Him most of all. However the believer who is confident in the love of Christ will do what is right because it pleases Him ... and He will certainly reward that loyal love.