When some non-Christians (or some former Christians) consider the teaching that presents a clear and compelling understanding of the concept of hell, they may wonder why Christian faith emphasizes the idea of "hell" rather than the less-terrifying notion of "not being with God" in heaven. Why not simply state that those who never believed or rejected Christ after believing just don't experience the presence of God in eternity? This is an intriguing question. Here are a few possible reasons Christian faith seems to pay more attention to hell as compared to the concept of "not being with God."

1. The Scriptures Speak More Explicitly About Hell

It is important to highlight that both concepts are clearly mentioned in the Bible, although it could be argued that the idea of "absence of God" is not directly presented but can be inferred. However, the Christian tradition relies heavily on scriptural texts for doctrinal formulation. In this case, there are more verses that describe an explicit place called "hell" or the "Lake of Fire," than there are specific references that explicitly talk about an absence of God in heaven. Thus, there might be an emphasis on the first concept since it seems to be more explicit in what the scriptural text seems to teach. For instance, the following verses are obvious about the idea of hell, whereas finding parallels about the lack of presence of God in heaven in the scripture might be slightly difficult: “The Son of Man will send his angels, and they will gather out of his Kingdom all causes of sin and all lawbreakers, and throw them into the blazing furnace, where there will be weeping and gnashing of teeth.” (Matthew 13:49-50); "And another angel, with a golden incense jar, came and stood at the altar; and he was given much incense to offer, with the prayers of all the saints, on the golden incense jar, which comes from the throne of God. And the smoke of the incense, with the prayers of the saints, ascended before God from the angel’s hand." Here, contrastingly, the latter concept has less direct scriptural assertion.

2. It Is Inherent To Theological Discussions on Sin and Redemption

The Christian doctrine has a foundational structure grounded in the theology around sin, redemption, and grace. Concepts like judgment, repentance, and atonement come naturally embedded in this framework, and hence, as a necessary corollary, the biblical teaching about hell inevitably comes into view. In fact, the concept of “not being with God” (as some interpretational parallel) doesn't carry a full theological weight equal to the actual biblical tenet around Gehenna/Hell. Where hell, being a place of eternal punishment for the impenitent and disobedient, serves as one end of the theological spectrum of redemptive love and just judgment, the absence of God's presence is perceived as a side note in some theological discussions, rather than being a central theological topic in itself. Therefore, the picture of Hell might appear emphasized as it stems from the core of Christian belief, even though the 'lack of presence' notion, though understandable, does not occupy the same space in these theological conversations.

3. Evangelism, Apologetics, and Fear of the Lord

Another factor could be the historical aspect related to early Christian missionizing activities. Evangelists wanted people to pay heed to the message of salvation not just because it promised 'heaven', but also because of the stark realities of 'hell.' As a part of apologetic strategy, they used the doctrine of hell to underscore the dire consequences of rejecting the divine truth—to ignite fear and respect, often labeled as 'fear of the Lord', which is an acceptable pathos within Christian theology and its history. It's possible that this amplified emphasis on hell is tied to the missional strategies of early Christian communities.

While these various factors could account for why there appears to be an emphasis on hell over the concept of "not being with God" in terms of Christian discourse, it is also important to remember that hell serves as the clear opposite of the hope offered by Christ - who came to redeem and save us from such a fate. So while the absence of God’s presence as a theoretical concept could serve as a frightening alternative to some, it might be less poignant for many within the context of Christian doctrine.