I should say this up front: I don't believe in heaven as a spiritual plane of existence to which my consciousness will go after my death. The Bible presents a number of diverse views about the matter, revolving around words and phrases like "paradise" and "new creation" and "the heavens." I've learned to be gracious with other Christians who adhere to it because it's really not that important. I've learned to be especially gracious with fellow Christians who (intentionally or otherwise) centre their faith around the reward of "getting into heaven."
Amazing grace indeed.
Perhaps a strong, extra-biblical reason to discount belief in a heaven is the question of why God didn't get it right first time. If he can get it right a second time, why not get it right the first time and avoid all the evil along the way?
For me, the answer lies through interpreting the visions of the future (paradise, the day of the Lord, the second coming, the new creation, the kingdom of God) in the same way that we talk about what life ought to be like as lived here and now. The gospel is about how we should live now. I think it's easy to reduce Jesus down to the point of what he did for us on the cross. Even though that's a significant event, it's an over-simplification and also misses the point of the gospel.
I like that gospel should actually translate as message rather than good news. The gospel isn't all good news. It's got some bad news. Good news for the oppressed. Bad news for the oppressor. But what's the bad news? The bad news is that the oppressor, who gains by oppressing someone else, has to stop doing it and look after the oppressed.
Ouch. Sounds harsh. #sarcasm
And what's left when the gospel is enacted by humanity? The lamb (oppressed) can sit down with the lion (oppressor). The lowly are lifted up and the lofty are brought down so that they are equals before God and each other. The people at war with each other make peace and live peacefully. And so on and so on. Does it sound like a great idea? Absolutely. Can we do it today? Absolutely. That's the hope of the gospel and the faithful work of every Christian.
I think that the Bible doesn't tell us to wait until after we die to see this kind of reality. I think that it tells us to make it happen today.