Genesis chapter 4

It doesn't actually say in the bible why Cain's offering was not acceptable to God. I think, though, this is a case of Cain's heart not being right with God.

Amos 5: 21-24 “I hate all your show and pretence— the hypocrisy of your religious festivals and solemn assemblies. I will not accept your burnt offerings and grain offerings. I won’t even notice all your choice peace offerings. Away with your noisy hymns of praise! I will not listen to the music of your harps. Instead, I want to see a mighty flood of justice, an endless river of righteous living."

It’s not something that just happened with Cain, either. Throughout time, many have been guilty of giving half heartedly to God, of paying lip service to worship on a Sunday morning, their minds busy elsewhere whilst their lips are singing. God doesn't ask for part of us, a snippet on a Sunday morning, a few minutes here and there during the week. He wants all of us, body, mind and soul:

Mark 12: 33 To love him with all your heart, with all your understanding and with all your strength, and to love your neighbour as yourself is more important than all burnt offerings and sacrifices.

Maybe Cain had been having a really bad day. Maybe his crops had failed, he'd run out of seed and fertiliser, maybe he'd just had enough of scrimping and scraping in the ground to make a living, to grow food and provide for his family. We all have days like that. When whatever we do just takes far longer than we expect, when we hit problem after problem, when everything that could go wrong does, the car breaks down, we're late for a meeting, we forget a deadline, the children are being really obnoxious and disobedient, we are left to do everything ourselves and no one even considers offering to help, etc. But it is how we deal with days like that which distinguishes us from nonbelievers, or should do.

We need to take everything, no matter how big or small, to God, to turn to Him in prayer when we are having that rubbish day and when things go really well. God is not just God of our good days, but He is also God in our bad times. Conversely, it is not just a case of turning to God when things go wrong but of giving Him the praise and glory when things go well. We need to get our hearts right with God, to put Him first in our lives, not second, third, or even further down the list.
Cain didn't do this. He allowed his mood to colour his reactions, let his temper take over, with the result that he killed his own brother. A temper is a very powerful thing, and we can do things when in a real temper that we would never dream of doing normally. When we lose control like that anything can happen. But if we are walking with God, talk with him daily, spend time in prayer and bible study, then this is less likely to happen, because our thoughts and mind will naturally be set on the things of heaven and not of this world. If Cain had been closer to God, maybe things would have turned our differently.

Isaiah 12:2 Surely God is my salvation; I will trust and not be afraid. The Lord, the Lord, is my strength and my song; he has become my salvation.