One person esteems one day as better than another, while another esteems all days alike. Each one should be fully convinced in his own mind.  The one who observes the day, observes it in honor of the Lord. The one who eats, eats in honor of the Lord, since he gives thanks to God, while the one who abstains, abstains in honor of the Lord and gives thanks to God. (ESV)
Christians have very different ideas when it comes to their freedom as believers. The context of these verses is the Christians who had a Jewish background and now were free from the obligations of the ceremonial law which had requirements regarding Sabbaths and Feasts. The Gentiles did not want to fall back into special days and festivities related to his previous way of life.
For the Christians who had a Jewish background it was important that they be careful how they observed days. If they felt obligation to celebrate feasts and Sabbaths they were forgetting the wonderful grace of God that set them free. If they chose to celebrate those same days as a way of freely honoring the Lord it would have been fine. They were to be convinced in their own mind.
For the Gentiles who came to the Lord after living a life of pagan idolatry it was important for them to realize that they were able to set aside days of worship and fellowship that were not the same as the previous pagan attachments. Just like the Christians of Jewish background it was important for them to observe days as unto the Lord. It was between them and the Lord to decide.
The big problem where Christians get into trouble is that they try to make up someone else's mind instead of making up their own mind as to what days ought to be honored. We can come to a different conclusion than our brother or sister without destroying them. If we are being thankful and honoring the Lord we will not be unloving toward our brother or sister in the Lord.
Do you find yourself constantly arguing with other Christians who disagree with you on minor points of theology? Are you fixated on changing people's opinions on non-important issues? Ask God to help you to mind your own business!