In this passage we are to esteem others higher than ourselves. By putting on the mind of Christ we decide to put others first and become true servants.
As a Christian we completely give up our own will and take on Christ’s. So we should want to serve others. Galatians 5:26 says not to desire vain glory or provoke/envy one another. Galatians 5:13-15 says to serve one another in love and love your neighbor. To do this we must be more concerned about others. Romans 12:10 says to “give preference to one another.” 1 Corinthians 10:24 says “Let no man seek his own, but every man another’s wealth.” 1 Corinthians 13:5 says that love does not insist on its own way, suggesting we should not do so either. Hebrews 10:24-25 as well tells us to consider one another and to exhort one another. This is to help get each other to heaven.
As you can see we have example after example showing we should put others first. Not too mention we should strive to be like Jesus and he was the perfect example of selflessness and servanthood. And there are other biblical examples. So we can see the importance of putting others first.