“Haven’t you read that at the beginning, the Creator ‘made ...” (Matthew 19:4-6)

Some Pharisees came to him to test him. They asked, "Is it lawful for a man to divorce his wife for any and every reason?" "Haven't you read," he replied, "that at the beginning the Creator 'made them male and female,' and said, 'For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh'? So they are no longer two, but one flesh. Therefore what God has joined together, let no one separate." (Matthew 19:4-6)

Why were the Pharisees testing Jesus?

The reason this was a test is that the temple organization of Pharisees and Sadducees had a strict code of ethics at that time, that had been interpreted from the scripture of the prophets. We can contrast this with Jesus’ comment about Moses, pointing out that Moses’ law was based upon the situation and circumstances among that particular society:
“Moses permitted you to divorce your wives because your hearts were hard." (Matthew 19:8)
This illustrates the importance of time and circumstance when it comes to the teachings of God's representatives. The time and circumstance and current society as these teachings are to be considered.

Yet at the same time, there are parts of their teachings that apply universally, regardless of the time and circumstance. The primary of these was taught by Moses and Jesus:
"'Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment. And the second is like it: 'Love your neighbor as yourself.' (Matthew 22:37-39)
Jesus did not make up this teaching. He was quoting Moses, from Deuteronomy 6:5. This was also Moses' central teaching. Moses restated this elsewhere:
"Love the LORD your God and keep His requirements, His decrees, his laws and His commands always." (Deuteronomy 11:1)

"So if you faithfully obey the commands I am giving you today—to love the LORD your God and to serve Him with all your heart and with all your soul—" (Deut. 11:13)

"If you carefully observe all these commands I am giving you to follow—to love the LORD your God, to walk in obedience to him and to hold fast to Him—" (Deut. 11:22)

"because you carefully follow all these laws I command you today—to love the LORD your God and to walk always in obedience to Him—then you are to set aside three more cities." (Deut. 19:9)

"For I command you today to love the LORD your God, to walk in obedience to Him, and to keep His commands, decrees and laws; then you will live and increase, and the LORD your God will bless you in the land you are entering to possess." (Deut. 30:16)

"and that you may love the LORD your God, listen to His voice, and hold fast to him. For the LORD is your life, and he will give you many years in the land he swore to give to your fathers, Abraham, Isaac and Jacob." (Deut. 30:20)

"But be very careful to keep the commandment and the law that Moses the servant of the LORD gave you: to love the LORD your God, to walk in obedience to him, to keep his commands, to hold fast to him and to serve him with all your heart and with all your soul.” (Joshua 22:5)

"So be very careful to love the LORD your God." (Josua 23:11)
We see from the last two verses that Joshua - who was Moses' student - also taught this principle. All of the Prophets also taught this - though some were misquoted as teaching to "fear God" - translated from the Hebrew word יָרֵא (yare') - which also means to "revere" or "honor" or "be awed" according to the lexicon.

Why didn't Jesus accept their authority?

The question relates to authority. Jesus is questioning their authority to represent God and God's messengers as they are doing. 

Jesus is not accepting that they have the authority to represent God.

This position enables us to also question the authority of those who are today claiming they represent Jesus. Do they represent Jesus if they receive a seminary degree? Do they represent Jesus if they are elected or appointed to a post in an institution?

The question is whether a democratic or council process of electing a priest, pope, cardinal, minister, reverend, rabbi, imam, or whatever the title given is sanctioned by God. 

Outside of Jesus' teachings, this can be answered logically. Men have determined this process. Men have developed these organized assemblies, not God. And it is the men (and women) within these assemblies that are choosing their teacher.

Since men have elected or appointed those roles, we know those roles are not determined by God. Therefore they are not representing God.

Why not? The democratic process chooses teachers that teach what those people who chose them want them to teach.

But couldn't this also be what God will teach? Can't an assembly of people portray God's will?

Groups of people can't represent God by default. Because group decisions require negotiation and compromise, they cannot represent God's will. God's will is determined by God and it cannot be negotiated or compromised and remain God's will. God's will by definition comes from God. It cannot be negotiated or compromised.

We should also note that Jesus received his baptism from John the Baptist, who also taught outside the confines of any religious institution.

The reason why these Pharisees are testing Jesus is that they were trying to remove Jesus' authority. They were trying to discredit Jesus. Because Jesus’ teachings of love for God and doing the will of God threatened their organizational control over the people, they sought to damage his reputation by finding conflicts between his teachings and those of the prophets.

Unfortunately, they didn't realize that Jesus' authority didn't come from Jesus - it came directly from God:
“My teaching is not my own. It comes from the One who sent me." (John 7:16)