"and that in this matter no one should wrong his brother or take advantage of him. The Lord will punish men for all such sins, as we have already told you and warned you. For God did not call us to be impure, but to live a holy life." NIV translation
Sin is and will be punished even for those who believe in Jesus. This punishment does not affect salvation but is like a parent that disciplines their child. God called us to be pure and holy and so He corrects us and allows consequences for sin in order that we may grow.
"Therefore, he who rejects this instruction does not reject man but God, who gives you his Holy Spirit." NIV translation
If we do not want to be holy, then we are not going against man but against the will of God. He has given us the power to be holy through the gift of the Holy Spirit.
"Now about brotherly love we do not need to write to you, for you yourselves have been taught by God to love each other." NIV translation
God is love and only He can teach us to love each other. That understanding can only come when we accept Jesus Christ and the example of love that He gave us.
"Make it your ambition to lead a quiet life, to mind your own business and to work with your hands, just as we told you, so that your daily life may win the respect of outsiders and so that you will not be dependent on anybody." NIV translation
We all answer to God for our own words and actions so we do not need to get involved in arguments and strife. We are to work and be an example for those that do not know Jesus.
"Brothers, we do not want you to be ignorant about those who fall asleep, or to grieve like the rest of men, who have no hope." NIV translation
We have hope through Jesus Christ and that hope is that we will be with God forever. For those that die here on earth (fall asleep), it is better to go on to be with the Lord. If we know that someone who died had accepted Jesus Christ, then we have no reason to mourn like the people that do not have our hope.