“Neither will I tell you by whose authority I do these things.” (Mark 11:33)

The Temple officials were demanding Jesus tell them by whose authority he was teaching and healing. Here is the full conversation:
Then they traveled again into Jerusalem and as he was walking in the Temple the chief priests, scribes and elders approached him – and they asked him, “By what authority do you do these things? And who gave you this authority to do these things?” Jesus replied, “I also ask of you one question – and if you answer me I will tell you by what authority I do these things. The baptism of John – was it from the spiritual realm – or of men? Answer me this.” They debated this among themselves, saying, “If we say ‘From the spiritual realm’ he will say, ‘Why then did you not believe him?’ But if we say, ‘Of men’ …” – as they feared the people, because everyone considered John to be a genuine Prophet. So they answered, saying to Jesus, “We don’t know.” Jesus answered them back by saying, “Neither will I tell you by whose authority I do these things.” (Mark 11:28-33)

Why did Jesus ask them this?

Because the Temple officials were not willing to admit that John's teachings came from the spiritual realm, Jesus was unwilling to respond to their request. Why not?

Because John's authority came from the Supreme Being. When Jesus said, "from the spiritual realm" he was indicating the authority coming from God, because the spiritual realm is where God personally dwells. A number of Biblical translations use the word "heaven" here, but the Greek word οὐρανός (ouranos) means, "the region above the sidereal heavens, the seat of order of things eternal and consummately perfect where God dwells".

Whatever we may call it, Jesus' reference to the spiritual realm indicates that he is clearly stating that John's authority and Jesus' authority come from the same person: The Supreme Being.

Is Jesus saying that he is God's representative?

In other words, Jesus is representing God. And John the Baptist also represented God. Jesus clearly indicates elsewhere that he is God's representative:
Truly I say to you, he that hears my teachings and trusts in Him who sent me, has eternal life and will not be judged, but crosses over from death into life." (John 5:24)
By myself I can do nothing; As I hear, I make choices, and my choices are just because I do not seek to please myself but to please Him who sent me." (John 5:30)
For the work that the Creator has given me to finish — the very work I am doing — indicates the Creator has sent me." (John 5:36)
For I have descended from the spiritual realm not to please myself but to please Him who sent me." (John 6:38)
“My teaching is not mine, but comes from He who sent me." (John 7:16)
I have many opinions I could say about you, but He who sent me is real; and the things I have heard from Him are the things I speak to the world.” (John 8:26)
These and many other statements by Jesus indicate clearly that Jesus was sent by God. Jesus is representing the Supreme Being. Being "sent" by someone else, and then speaking on behalf of that person is clearly the definition of being that person's representative.

For example, the President of a country might send his press secretary to a press conference to speak on his behalf. This is the reason why all the press people are asking the press secretary the things they wanted to ask the President: Because the Press Secretary is the representative of the President.

When such a Press Secretary comes before the press in the press conference, everyone accepts that the Press Secretary's authority is coming from the President. Otherwise, the press would pay no attention to the guy.

What would happen if, for example, a random guy off the street sneaks into the press conference and gets up on the mic and announces that he is the President's representative? It would quickly become known that this man doesn't represent the President. Or the President himself would denounce him.

In the same way, anyone can claim to be God's representative. This, in fact, is why the Temple priests and elders were so adamant about Jesus' authority. They figure that they have the authority. Why?

Because they were officially appointed and authorized by the officials of the Temple. They were basically elected into that position of priest or elder.

Let's consider this carefully. Using our press conference analogy, let's say that a man off the street walks into the press conference and goes before the press people and says, "how many of you will elect me to the post of the President's representative - the Press Secretary?" Then a majority of the press people raise their hands. So the man now claims he is the Press Secretary and he is now representing the President.

Could this really work like that? No. What is missing from this process?

The President. If someone claims to represent the President, then that person should be authorized by the President - right? That man off the street who was voted in might never even have met the President. Someone like this certainly can't claim to represent the President. He doesn't even know him. He certainly wasn't authorized by the President.

As a result, even if all the press people voted the man to the position unanimously, the man could never represent the President. Unless the President authorizes him to be the President's representative.

It is the same with all the various sects - all the churches and temples and mosques throughout the world whose leaders are elected or appointed to their posts. Those elected or appointed leaders are not representing God just because some people voted them in. They also cannot be representing God just because the previous (elected) priest appoints them.

The only way a person can achieve the position of representing the Supreme Being is if God authorizes that person. It is not that other people can elect them. Even if those people are also appointed or elected people - such as in the case of cardinals and bishops.

All of these sectarian priests that have been appointed or elected through political processes are thus disqualified from being God's representatives.

It is not just because they were elected or appointed. Certainly, God could also authorize a person who was also elected or appointed.

Does God authorize such people?

How do we know? Because people who undergo the process of getting elected or appointed are automatically disqualified. Because they underwent the process.

By allowing oneself to undergo such a process of election or appointment to a supposed position of representing God (priest, rabbi, reverend and so on) a person disqualifies themselves because they are offending God by undergoing the process.

By undergoing or accepting the process of appointment or election by people to the position of supposedly representing God, a person is stating that God cannot authorize His representative Himself. By undergoing or supporting such a process, a person is rejecting that the Supreme Being is Supreme: That God has the ability to select someone to represent Him.

By undergoing or accepting the process of appointment or election of someone to the position of supposedly representing God, such a person is stating that God has no power or authority to do this Himself. They are claiming that God cannot dispatch a representative. They are saying that because God has no power or authority to do it Himself, they have to intercede with their appointment or election process to determine which person supposedly represents God.

The bottom line is that God can and does authorize representatives who speak on His behalf. We know this because Jesus demonstrated that he was God's representative. And in this exchange Jesus demonstrates that John the Baptist was also God's representative. Neither was appointed or elected by any official church. Rather, they were authorized by the Supreme Being. Here is a clear statement by God to Jesus' disciples:
While he was still speaking, suddenly a bright cloud overshadowed them and immediately a voice came from the cloud, saying, “This is my beloved Representative, with whom I am well pleased. Listen to him!” (Matt. 17:5)
We also know by Jesus' statement that God doesn't just send one representative - e.g., Jesus. God has sent representatives to the world in every generation. This is seen clearly in the Old Testament in the form of the Prophets. There, we see Prophets from every generation teaching on behalf of the Supreme Being.

Jesus illustrated this because as Jesus taught the people, he often quoted the teachings of the Prophets. Why? Because they were all representing God. This is why Jesus could quote them in his teachings that represented God.

This also goes for the most important teaching - as Jesus quoted Moses from Deuteronomy 6:5:
“ ‘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." (Matt. 22:37-38)