What was he saying, or claiming?

Christ also said “Not by my power, but by the Holy Spirit.” He is the intercessor for us. He is saying that nothing is possible without God. God gives all power and Christ’s power comes though God.

It was an expression of humility; and directed the compliment to G-d. Add this to bottlerocket’s on-point explanation.

To address the second part – “none is good save for”...

This implies that people’s goodness is derived from G-d, whether they believe in Him or not.

Now behold, one came and said to Him, “Good Teacher, what good thing shall I do that I may have eternal life?’’ So He (Jesus) said to him, “Why do you call Me good? No one is good but One, that is, God. But if you want to enter into life, keep the commandments.’’ (Mt 19.16–17; also Mk 10.18, Lk 18.19)

In the passage quoted above, a rich man came to Jesus in order to find out how to have eternal life…
Now behold, one came and said to Him, “Good Teacher, what good thing shall I do that I may have eternal life?’’ (Mt 19.16)
It is clear that the rich man had no idea of the fact that Jesus is the Messiah, the Son of God.
Rather, the rich man regarded Jesus as being merely a Rabbi—a teacher of religious principles…

Now behold, one came and said to Him, “Good Teacher…” (Mt 19.16a)
Obviously the rich man believed that Jesus had Himself obtained eternal life. If the rich man hadn’t believed that, he would never have come to Jesus for advice on how to go to heaven.
Moreover, the rich man believed that Jesus had earned eternal life because Jesus was a “good” person…
Now behold, one came and said to Him, “Good Teacher…” (Mt 19.16a)
In summary, the rich man was sorely in error on three vital points…
Error #1 – The rich man thought Jesus was merely a man—a great teacher, yes—but merely a man.
Error #2 – The rich man thought this “mere man” had achieved such a degree of “human goodness” that He had EARNED eternal life in Heaven.
Error #3 – Accordingly, the rich man believed that he, too, could earn eternal life merely by doing good deeds under his own steam…
Now behold, one came and said to Him, “Good Teacher, what good thing shall I do that I may have eternal life?’’ (Mt 19.16)
Because the rich man was measuring the goodness of Jesus according to merely human standards, Jesus responded as follows…
So He said to him, “Why do you call Me good? No one is good but One, that is, God. (Mt 19.17)
When Jesus said, “Why do you call me good?” He was merely asking a question in order to teach.
He was not saying, “I am not good.”
Rather, He was saying, “Don’t assess anyone’s goodness based on human standards of goodness.”
Then Jesus immediately told the rich man that the ONLY standard of goodness is God Himself…
So He (Jesus) said to him, “Why do you call Me good? No one is good but One, that is, God. (Mt 19.17)
Thus, Jesus taught the rich man the same lesson He had taught in His “Sermon on the Mount” (Matthew chapter 5
Namely, “good” isn’t good enough. You have to be as perfect as God Himself…
(Jesus said…) Therefore you shall be perfect, just as your Father in heaven is perfect. (Mt 5.48)
The main point that Jesus taught the rich man was that he couldn’t achieve God’s state of perfection. Therefore, he couldn’t obtain eternal life by his own good works.
The bottom line—eternal life can be obtained only as an out-and-out gift from God, through faith in Jesus…
Jesus said to him, “If you want to be perfect, go, sell what you have and give to the poor, and you will have treasure in heaven; and come, follow Me.’’ (Mt 19.21)
For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, lest anyone should boast. (Eph 2.8–9)

Who that’s a very long answer. I can see how people get overwhelmed in choosing their faith. You appear to be saying Jesus was not saying that he is not good.
“Why do you call me good?” He was merely asking a question in order to teach. yes I can see it’s a question, but he also makes a statement.“No one is good but One, that is, God.”
So either he is God or he’s not good. So which is he saying or claiming?

It’s clear the rich man believed there must be something he could DO to earn eternal life.

Jesus gave him two things to do for for eternal life and treasures in heaven.

But if you want to enter into life, keep the commandments.
“If you want to be perfect, go, sell what you have and give to the poor, and you will have treasure in heaven; and come, follow Me.’’