"HERE I AM, I AND THE CHILDREN WHOM GOD HAS GIVEN ME."

 12 saying,

"I WILL DECLARE YOUR (the Father's) NAME TO MY BRETHREN (believers),

IN THE MIDST OF THE CONGREGATION I WILL SING YOUR PRAISE."

13 And again [He says],

"MY TRUST and CONFIDENT HOPE WILL BE PLACED IN HIM."

And again,

"HERE I AM, I AND THE CHILDREN WHOM GOD HAS GIVEN ME."—Hebrews 2:12-13

During His sojourn here on earth, Jesus depended completely on His Father just as we must as believers during our own.  Here (in verse 12 which is quoted from Psalm 22:22), He fully identifies with mankind by calling them His brethren. In Matthew 12:49-50, Jesus teaches that whoever does the will of the Father are His brother, sister and mother.

And stretching out his hand toward his disciples, he said, "Here are my mother and my brothers! 50 For whoever does the will of my Father in heaven is my brother and sister and mother." (Matthew 12:49, ESV)

However, Jesus does not directly call them brethren, until after His resurrection. 

Jesus said to her, "Do not cling to me, for I have not yet ascended to the Father; but go to my brothers and say to them, 'I am ascending to my Father and your Father, to my God and your God.'" (John 20:17, ESV)

With all that said, what struck me about Hebrews 2:13 was that Jesus IS my big brother who came to this earth to die, and in so doing provided redemption for me —His little sister.  Jesus by His death FREED ME from the haunting ( a very accurate word) fear of death which prior to my salvation held me captive.  Hebrews 2:14-15 describes it this way:  

Therefore, since [these His] children share in flesh and blood [the physical nature of mankind], He Himself in a similar manner also shared in the same [physical nature, but without sin], so that through [experiencing] death He might make powerless (ineffective, impotent) him who had the power of death—that is, the devil— 15 and [that He] might free all those who through [the haunting] fear of death were held in slavery throughout their lives.

Jesus extends to us, fallen human beings, His good hand of deliverance.  To do that, it was essential that He be made like us, His brethren in every way.   Verse 2:17-18 in the Amplified version explains the why of this well. 

so that He might [by experience] become a merciful and faithful High Priest in things related to God, to make atonement (propitiation) for the people's sins [thereby wiping away the sin, satisfying divine justice, and providing a way of reconciliation between God and mankind].  18 Because He Himself [in His humanity] has suffered in being tempted, He is able to help and provide immediate assistance to those who are being tempted and exposed to suffering

The beauty of what Jesus, my Brother, did for me and for you...the children that God has given Him...is truly indescribable.  Death no longer brings fear because fear involves torment.  God’s love toward me...toward you...is perfect.  Death has been swallowed up in victory. 

When the perishable puts on the imperishable, and the mortal puts on immortality, then shall come to pass the saying that is written: "Death is swallowed up in victory." "O death, where is your victory? O death, where is your sting?"  The sting of death is sin, and the power of sin is the law.  But thanks be to God, who gives us the victory through our Lord Jesus Christ.  Therefore, my beloved brothers, be steadfast, immovable, always abounding in the work of the Lord, knowing that in the Lord your labor is not in vain. (1 Corinthians 15:54-58, ESV) (emphasis mine)

Inasmuch then as we [believers] have a great High Priest who has [already ascended and] passed through the heavens, Jesus the Son of God, let us hold fast our confession [of faith and cling tenaciously to our absolute trust in Him as Savior]. For we do not have a High Priest who is unable to sympathize and understand our weaknesses and temptations, but One who has been tempted [knowing exactly how it feels to be human] in every respect as we are, yet without [committing any] sin. Therefore let us [with privilege] approach the throne of grace [that is, the throne of God's gracious favor] with confidence and without fear, so that we may receive mercy [for our failures] and find [His amazing] grace to help in time of need [an appropriate blessing, coming just at the right moment].—Hebrews 4:14-16 AMPLIFIED