They did not like paying taxes. The government was foreign and oppressive. Money was not so plentiful they could happily give up part of what they had. What they wanted to hear was a religious excuse from taxes. What they got was a gentle reprimand.
According to Matthew 22:21 we are to “Render therefore unto Caesar the things which are Caesar’s; and unto God the things which are God’s.” A country’s money most often bears the image of the nation’s leaders or former leaders. If this was Jesus’ way of telling the people to pay their taxes to the government who had issued the coins, couldn’t we assume it was also His way of reminding us to commit our lives to our Creator?