The disciples had left the bread behind (Matthew 16:7); so when Jesus talked about the 'yeast of the Pharisees and Sadducees' (Matthew 16:6) they thought He was criticising their failure.  They did not want to be shamed by the Lord (Matthew 14:31) and tried to please Him.  However, His holiness was a continual reminder of their sinfulness, giving them an inner urge to do better but also the sinking realisation that they could not meet His standard.
 
They had not understood that nobody can get everything right, even if they lived and worked alongside Jesus.  Their minds were saturated by religious rules; they believed that if they could be better, they would be accepted … just like the religious leaders who opposed their Master.  They had no concept of grace – goodness given and forgiveness offered without having earned it.  Jesus had recently demonstrated His grace, producing bread and giving it away to 4000 families without any charge (Matthew 15:29-38).  He is the Giver of grace (1 Corinthians 1:4).
 
Jesus wanted to warn them against the 'non-grace' of Christless religion, and they had just fallen into the trap He wanted them to avoid.  The malignant virus which fuels every Christless religion is the belief that keeping the rules will win God's favour, and that failure will exclude people from His kingdom.  It was how the religious rulers maintained their power over the people; locking them into a system of rules they could not keep; encouraging a personal obsession to try harder, and yet knowing they could never fully succeed.  Unless God gives His righteousness, nobody can stand blameless before Him.  That is why we need to admit our weakness and dare to receive His grace (2 Corinthians 12:9).
 
These religious ideas are woven into the fabric of most societies.  They are learned as children and yet repeated failure drives many adults away from the 'faith' - because they find it impossible to keep the rules.  Jesus came to give us His grace: goodness and forgiveness we could never deserve (Ephesians 2:8-9).  'Faith' is not about believing that we can succeed to keep the rules; it is about believing that through Jesus we can be freely forgiven, and then freely be given all that we need to serve Him.  This is the gospel: share it with people who have given up on their own ability to be good; share it with those who are exhausted by trying and perpetually disappointed by their failures; and preach it to yourself!