Peter wrote a letter to a suffering church. Roman power was orderly but corrupt. To work within the system, you would give and take bribes, wink for the right people, etc. The church was radical to some degree: The people claimed a King other than Caesar. They resisted the corruption of the system.
When you step out of the cultural system, especially when it is corrupt, you are likely to get negative feedback. History tells us that the early church was widely accused of cannibalism and shunned from the rest of society. Many were imprisoned and martyred.
The government was not kind to them, and yet Peter gave them some advice that defied common sense. He told them to submit to the powers that were above them and work within the system. He implored them to be the best citizens they could, so that no one could find fault with them.
When we are persecuted and mistreated, the Christian response is to turn the other cheek. In addition, to those in authority, we are to submit to their rule, trusting God to give us justice. God delivered the Israelites out of slavery, and he will deliver us too. Think of someone like Martin Luther King Jr: He fought systemic government injustice through a peaceful process of protest. It cost him his life. This is a good Christian response.
The next time you feel mistreated, think about Jesus' suffering. He took the pain of the cross for the benefit of people who hated him and killed him. Then, think about your own suffering and ask Jesus what you should do.