So, when God gave His only-begotten son to save the world, how can people still believe in the Trinity?

I believe in the Trinity because it follows deductively from several passages in the Bible.

The Father is greater than the Son in the sense of being functionally subordinate to the Father, not in the sense of being a lesser being.

A good analogy is 1 Corinthians 11:3, which says, "But I want you to understand that Christ is the head of every man, and the man is the head of a woman, and God is the head of Christ." If God is the head of Christ in the same sense that men are the heads of their wives, then in what sense are men the head of their wives? Women are not inferior beings to men. They are exactly the same kind of being. They have equal value and worth, and they are equal inheriters of eternal life. The relationship between them is one of functional subordination. It is in THAT sense that men are the head of their wives, and it is in THAT sense that God is the head of Christ.

The passage in Proverbs 8:22 does not refer to Jesus. It refers to Wisdom personified. It's just a poetic analogy. It doesn't refer to a person at all. Just read the whole chapter, and you'll see that.

God is ONE: One being, three persons. A human is one being and one person: A cat or dog is one being and NO persons: God is one being and THREE persons. We can not FULLY understand the Trinity, but the scripures are pretty plain that God IS Trinity:

Jesus tells his apostles to baptize "in the name [notice, singular, not plural] of the Father and of the Son and of the Holy Spirit" (Matt. 28:19). This is a proof-text: three distinct Persons united in the one divine name. In 2 Corinthians 13:14, Paul writes, "The grace of the Lord Jesus Christ and the love of God and the fellowship of the Holy Spirit be with you all." We see this same unity of divine Persons in 1 Corinthians 12:4–11, Ephesians 4:4–6, and 1 Peter 1:2–3.

The Bible clearly teaches that Jesus is God (cf. John 8:58, 10:38, 14:10; Col. 2:9). It also clearly teaches that the Holy Spirit is God (cf. Acts 5:3–4, 28:25–28; 1 Cor. 2:10–13). Everyone agrees the Father is God. Yet there is only one God (Mark 12:29, 1 Cor. 8:4–6, Jas. 2:19). How can we hold all four truths except to say all three are One God?

And yes, Jesus DID say he was God. In John 8:58, when quizzed about how he has special knowledge of Abraham, Jesus replies, "Truly, truly, I say to you, before Abraham was, I Am"—invoking and applying to himself the personal name of God—"I Am" (Ex. 3:14). His audience understood exactly what he was claiming about himself. "So they took up stones to throw at him; but Jesus hid himself, and went out of the temple" (John 8:59).

Also significant are passages that apply the title "the First and the Last" to Jesus. This is one of the Old Testament titles of Yahweh: "Thus says Yahweh, the King of Israel and his Redeemer, Yahweh of armies: ‘I am the First and I am the Last; besides me there is no god’" (Is. 44:6; cf. 41:4, 48:12).

People want an image of God. They figure they can call Jesus, God; then get away with it. God the is the Father and number ONE. Jesus is the son that is in charge of us now; but will step down when the time comes. And we must still send all our prayers to God only. And God made the Holy Ghost for us that really believe.

So God created all and is on top of the triangle. Jesus and the Holy Ghost, God created both and have giant jobs, are the two points in the lower area of the triangle.

Eph 3:9 And to make all [men] see what [is] the fellowship of the mystery, which from the beginning of the world hath been hid in God, who created all things by Jesus Christ:

God tells angels to worship Him:

6 And again, when God brings his firstborn into the world, he says,

"Let all God's angels worship him." (Hebrews 1 & Psalm 45)

God calls Jesus God:

8 But about the Son he says,

"Your throne, O God, will last for ever and ever,

and righteousness will be the scepter of your kingdom.

9You have loved righteousness and hated wickedness;

therefore God, your God, has set you above your companions

by anointing you with the oil of joy."

(Hebrews 1 & Psalm 45)

Jesus says that God is Spirit:

24 God is spirit, and his worshipers must worship in spirit and in truth." (John 4)

Jesus calls God the Father:

John 20:17

Jesus said, "Do not hold on to me, for I have not yet returned to the Father. Go instead to my brothers and tell them, 'I am returning to my Father and your Father, to my God and your God.' "

Jesus says that the Father and him are one:

30 "I and the Father are one."

Jesus calls himself 'from everlasting to everlasting ':

58"I tell you the truth," Jesus answered, "before Abraham was born, I am!" (John 8)

Jesus is in Daniel 7 as the Most High, having a separate set of independent actions from the Ancient of Days:

13 "In my vision at night I looked, and there before me was one like a son of man, coming with the clouds of heaven. He approached the Ancient of Days and was led into his presence. 14 He was given authority, glory and sovereign power; all peoples, nations and men of every language worshiped him. His dominion is an everlasting dominion that will not pass away, and his kingdom is one that will never be destroyed.

21 As I watched, this horn was waging war against the saints and defeating them, 22 until the Ancient of Days came and pronounced judgment in favor of the saints of the Most High, and the time came when they possessed the kingdom.

I studied Theology and have a degree in it so I am familiar with all of the religions and faiths. People believe in the what speaks to their heart and aligns with their beliefs. And, since the books that speak about religion were written by man, and man is faulty and with subjectivity, there is a possibility that what is written is not what was actually meant by the religious figure or deity. Therefore, to believe something is to feel it with your heart and not with your head.

The Earliest of Christians believed in the Trinity!

You think you know more than them?

See http://www.bcbsr.com/topics/jdeity.html

http://www.bcbsr.com/topics/trinit.html