This crowd looked like they were seeking Jesus, but they were actually trying to use Jesus to seek their own end. It is true that there are many personal benefits to be reaped through serving the Lord, but the benefits are never to become our reason. Christ must be first in everything (Colossians 1:18).
Jesus exposed the true intent of the people's hearts by preaching a strong message of commitment. Those who were self-centered were offended and left while those who were willing to lay down their lives to experience God's abundant life remained.
Commitment to God Himself (not what He can give) is what always separates the true worshippers of God from the false.
As Jesus began to explain in these verses that He was the only way to the Father (John 14:6) and that they would have to come through Him, the people got angry. It always angers the flesh to think that all our righteous acts can't save us, but Jesus made it clear that our only part in salvation is to believe. Believe what? Believe on Jesus and His sacrifice, not our works. Salvation is a gift and cannot be purchased (Romans 10:2-3).
Many times, we get so intent on seeking God in one area that we forget the greatest miracle of all, which is the love and redemption given to us from God through His Son. God loves us so much!