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"Humble" here in verse 6 is from the Greek word tapeinoo. It means "to make low" and it can be used literally, as of mountains and hills being brought low, or it can be used metaphorically, as in abasing, being abased, to be abased, to humble yourselves. It includes being gentle, patient and mild. It is the opposite of proud, or what we might call today "stuck-up." Romans 1:30 calls these kinds of people "proud" or "arrogant."
In His great love, God sees all of us as lost sheep going astray. We should see each other with the same love as God sees us. No one is greater than another--all have sinned and fall short of the glory of God (Romans 3:23). All are brought low before God in our sins, and only God can raise us up--not as haughty, proud or arrogant people to "lord it over others that we are saved," but as sons of God, His children by His grace, seen through the blood of His Son.
"God opposes the proud but gives grace to the humble" is a quotation from Proverbs 3:34. Jesus put it this way:
"But you are not to be called ‘Rabbi,' for you have only One Master and you are all brothers. And do not call anyone on earth ‘father,' for you have One Father, and He is in heaven. Nor are you to be called ‘teacher,' for you have One Teacher, the Christ. The greatest among you will be your servant. For whoever exalts himself will be humbled, and whoever humbles himself will be exalted," (Matthew 23:8-11).
Consider the following Scriptures about the children of God being humble before the Lord and one another:
James 4:7-10: "Submit yourselves, then, to God. Resist the devil, and he will flee from you. Come near to God and He will come near to you. Wash your hands, you sinners, and purify your hearts, you double-minded. Grieve, mourn and wail. Change your laughter to mourning and your joy to gloom. Humble yourselves before the Lord, and He will lift you up."
1 Peter 5:5-11: "Young men, in the same way be submissive to those who are older. All of you, clothe yourselves with humility toward one another, because, ‘God opposes the proud but gives grace to the humble.' Humble yourselves, therefore, under God's mighty hand, that He may lift you up in due time. Cast all your anxiety on Him because He cares for you. Be self-controlled and alert. Your enemy the devil prowls around like a roaring lion looking for someone to devour. Resist him, standing firm in the faith, because you know that your brothers throughout the world are undergoing the same kind of sufferings. And the God of all grace, Who called you to His eternal glory in Christ, after you have suffered a little while, will Himself restore you and make you strong, firm and steadfast. To Him be the power for ever and ever. Amen."
This is how we approach God in prayer--with humility, constantly being aware of the fact that we could not save ourselves, and that only HE could make us into something worthwhile--His dearly loved children:
2 Chronicles 7:14: "if My people, who are called by My Name, will humble themselves and pray and seek My face and turn from their wicked ways, then will I hear from heaven and will forgive their sin and will heal their land."
Ephesians 5:1: "Be imitators of God, therefore, as dearly loved children and live a life of love, just as Christ loved us and gave Himself up for us as a fragrant offering and sacrifice to God."
Colossians 3:12-14: "Therefore, as God's chosen people, holy and dearly loved, clothe yourselves with compassion, kindness, humility, gentleness and patience. Bear with each other and forgive whatever grievances you may have against one another. Forgive as the Lord forgave you. And over all these virtues put on love, which binds them all together in perfect unity."