God wants us to love Him with all our heart, soul, mind, and strength. Sacrifice and offerings were ways through which the Israelites expressed their love for God. But the Israelites began to worship other gods (commit spiritual adultery) while continuing the rituals of sacrifice and offerings without love for God. It's hypocrisy. Hosea 6:4 talks about their faithfulness fading away (disappearing). Without inward love/mercy and acknowledgment of God, the outward rituals are meaningless to Him. The sacrifice and offerings are worthless without an undivided heart that is completely devoted to God and that loves and acknowledges God.
People often acknowledge talents, accomplishments, hard work, success, beauty, intelligence, even luck/fortune and Mother Nature. But they fail to realize/recognize Who is the Giver of all blessings...Who created us and nature...Who is sovereign over all things, Who is behind all the miracles, etc. And we ourselves like to be acknowledged, don't we? That's why we need to be careful to remember that anything good in us is what the Lord has done for us, in us, and through us. If we fail to acknowledge God, our good deeds/service/giving/ministries ("burnt offerings") mean nothing.
God's mercy is so great and He desires us to extend His mercy to others. "Be merciful, just as your Father is merciful." (Luke 6:36 ) We are to resemble/imitate Him, the merciful God. Jesus later used Hosea 6:6 to teach against the hypocritical Pharisees. Jesus said in Matthew 9:12-13, "It is not the healthy who need a doctor, but the sick. But go and learn what this means: 'I desire mercy, not sacrifice.' For I have not come to call the righteous, but sinners." When the Pharisees complained to Jesus about His disciples picking and eating heads of grain on the Sabbath, Jesus said, "If you had known what these words mean, 'I desire mercy, not sacrifice,' you would not have condemned the innocent." (Matthew 12:7) The Pharisees cared about the religious activities but neglected what really matters (what God desires). "The Lord says: 'These people come near to Me with their mouth and honor Me with their lips, but their hearts are far from Me. Their worship of Me is based on merely human rules they have been taught.'" (Isaiah 29:13)
Remember...God looks at the heart. If our heart lacks steadfast love/mercy and does not acknowledge God, all our sacrifice and "burnt offerings" (any form of offerings) would be detestable to Him. External piety such as fasting, going to church, giving tithes, partaking the Lord's supper, etc. is no substitute for genuine love, mercy, faith, and obedience.