The Trinitarian stance is that Jesus Christ was unarguably a man, “Son of Man” being his most-oft-used designation. It does not make sense for your question to add, “If the Pharisees were wrong in thinking Jesus was a man, why didn’t Jesus correct them, but instead reinforce that belief by calling himself ‘Son of Man’…”
No Trinitarian thinks the Pharisees were wrong to believe Jesus to be a man. Trinitarians also believe that Jesus was a man. He was fully man, but don’t be too hasty to add a full-stop there.
Second point about this question: There was nothing ‘simple’ about Jesus ‘just’ saying in public that he was God. For a start, that could be misleading (according to Trinitarian understanding of the complexity of the one Being of God). There is more to the one Being of God than the Word incarnate, made flesh, walking amongst other men who beheld his glory, that of the only-begotten of the Father (John 1:1-14). Jesus knew that if they didn’t understand that complex truth, they would instantly claim grounds for stoning him to death, but he had to complete his mission on earth. “My time has not yet come” he said several times during that mission. But when his time DID come, he went for it, telling those who hatefully asked him if he was “the Christ, the Son of the Blessed”, he said, “I am: and ye shall see the Son of man sitting on the right hand of power, and coming in the clouds of heaven.” (Mark 14:61-64)
This led to instant cries of “Blasphemy!” and they all condemned him as guilty of death.
That is why Jesus held back openly stating his deity until that moment, when his time had come. Stating that he was also the Son of God was too much for those who only thought him to be a man.
Third point about this question: Trinitarians understand why the Pharisees were offended at Jesus claiming (and showing) that he could forgive the sins of humans. The Pharisees only thought him to be a man. But had he only been a man, he could never have done the miracles he did, including raising the dead. So, to confound them, he gave that apparently indirect answer that stopped them in their tracks, forcing them to think about how he acted in conjunction with his claims, the former proving the validity of his claims to be able to forgive sins.
Jesus had to achieve the Father’s will before dying, and he knew that openly saying, “Oh, by the way, as well as being a man, I’m also God” would short-circuit the plan of redemption. Jesus had to arrive at the cross at just the right time, in just the right way. He did not enable the Pharisees to stone him to death for alleged blasphemy because he had to be hung on a tree to die, as accursed, the sinless sin-bearer.
It’s only when the Trinitarian explanation is applied that the full extent of the breath-taking enormity of just who Jesus is dawns, and then it becomes clear why it had to be God incarnate bearing our punishment for our sins that gets us on our knees in adoration. To say that it was only a man (even if a sinless man) dying for sinners makes no sense, for no man could ever achieve what Christ achieved – conquering death, and the one with the power of death, the devil – unless he were God incarnate. Christ “led captivity captive” in his train when he ascended “far above all heavens, that he might fill all things” (or, “fill the whole universe” NIV). Ephesians 4:7-10, which quotes Psalm 68:18, about God doing what Jesus did in the fulfilment, at his ascension. That is what it means to be Son of God. And that is why Jesus had to remain incognito, slipping in under the radar at his incarnation, and remaining discreet in what he disclosed to his mortal enemies, until his time had come – his God-appointed time to die, as a man, for sinners who would confess him as did doubting Thomas, “My Lord and my God!”