Someone who is not Catholic would follow the ancient practice of
haireomai: “to pick, to choose” (from which comes the term
heresy). This practice works as follows: one picks a passage in Scripture and focuses on it exclusively, ignoring the wholeness of Scripture, and its unity with Tradition; he thus forms his personal doctrine or judgment on the whole based on a part. This leads to errors and divisions.
A Catholic, instead, looks at the Deposit of Faith as a whole, including Scripture and Tradition, and if he focuses on an aspect, he understands it as a part of the whole. This preserves unity and allows truth to shine forth.
How could Christ by these words mean that He was not God, if later on, after His resurrection, He is addressed by his apostle s. Thomas as “my God” and He replies: “because you have seen you have believed…blessed are those who will not have seen and yet will believe”?
If He lets Thomas call Him God, and if He calls blessed those who will believe that He is God without having seen Him in person, radiant in His resurrected, glorified body, how could He mean the opposite when He stops a random person from calling Him good?
Was He not rather reminding that person that all goodness shines forth from God, and that even Him, in His goodness, was not good as a man, or as a teacher, but because of God?
In fact, the divinity of Christ shines from every action He does, if we find those actions in the Old Testament.
For instance:
(New Testament) Shortly before dawn Jesus went out to them, walking on the lake.
(Old Testament) The waters saw you, God, the waters saw you and writhed. …] Your path led through the sea, your way through the mighty waters, though your footprints were not seen. …]
(New Testament) A furious squall came up, and the waves broke over the boat, so that it was nearly swamped. … The disciples woke him and said to him, “Teacher, don’t you care if we drown?” He got up, rebuked the wind and said to the waves, “Quiet! Be still!” Then the wind died down and it was completely calm.
(Old Testament) And they cried to the Lord in their affliction: and he brought them out of their distresses. He stilled the storm to a whisper; the waves of the sea were hushed. Then they were glad because they were quiet, So He guided them to their desired haven.
(New Testament) Jesus replied, "Go back and report to John what you hear and see: The blind receive sight, the lame walk, those who have leprosy are cleansed, the deaf hear, the dead are raised, and the good news is proclaimed to the poor.
(Old Testament) He is the Maker of heaven and earth, the sea, and everything in them…He gives justice to the oppressed and food to the hungry. The Lord frees the prisoners. the Lord gives sight to the blind, the Lord lifts up those who are bowed down, the Lord loves the righteous. …] In that day the deaf will hear the words of the scroll, and out of gloom and darkness the eyes of the blind will see. …] Then will the eyes of the blind be opened and the ears of the deaf unstopped.
Another important aspect is His authority to forgive sins, which reveals His divinity (as the teachers of the law immediately noticed):
(New Testament)When Jesus saw their faith, he said, “Friend, your sins are forgiven.” And the scribes and the Pharisees began to question, saying, “Who is this who speaks blasphemies? Who can forgive sins but God alone?” …] And immediately when Jesus perceived in his spirit that they so reasoned within themselves, he said unto them …] the Son of man has power on earth to forgive sins
(Old Testament)But now, this is what the LORD says-- he who created you, O Jacob, he who formed you, O Israel: " …] I, even I, am he that blots out your transgressions for my own sake, and will not remember your sins."
Furthermore, the Lord is identified by the angel appearing to the Blessed Virgin Mary in the manner in which God reveals Himself to Daniel as “ancient of days” - a vision that Christ reaffirms before the Sanhedrin (further clarifying the divine and Messianic title of “son of man”, which in no way denies but rather reaffirms His divinity):
(New Testament)You will conceive and give birth to a son, and you are to call him Jesus. He will be great and will be called the Son of the Most High …] he will reign over Jacob’s descendants forever; his kingdom will have no end …]
“I adjure you by the living God, that you tell us whether you are the Christ, the Son of God.”
Jesus said to him, “You have said it: nevertheless I say to you, Hereafter you will see the Son of man sitting on the right hand of the power, and coming in the clouds of heaven.”
I saw in the night visions, and, behold, one like the Son of man came with the clouds of heaven, and came to the Ancient of days, and they brought him near before him.
And there was given him dominion, and glory, and a kingdom, that all people, nations, and languages, should serve him: his dominion is an everlasting dominion, which shall not pass away, and his kingdom that which shall not be destroyed.
All of this and much more was quite obvious to the teachers of the Law. They saw clearly that He acted in ways that unequivocally identified His divinity. They accused Him solely because they did not believe that He was the Messiah, but rather only a man, and thus He was blaspheming by acting in such ways. Had He been only a man, they would have been right.
(New Testament) The Jews answered [Pilate]: “We have a law, and by our law he ought to die, because he made himself the Son of God.” …] For this cause therefore the Jews were seeking all the more to kill Him, because He… was calling God His own Father, making Himself equal with God.
If you remain close to Him, you will always be confirmed in the faith 
As my favorite passage from the Night Prayer goes: “his faithfulness is buckler and shield”…not my faithfulness, nor your faithfulness…His faithfulness