Shouldn't the word translated as "church" in most modern Bible translations actually be "those set apart by God," making the "visible church" a total fabrication of man, and denominations and church buildings as they exist today an abomination to God?
Regarding the visible church discussed in our Revelation class, we can agree with your statement – to a point. Certainly, the word for Church in Greek is ekklesia, which means "of invited guests." The Church is a God-made entity comprised of those the Spirit of God invites into the faith. This is the only true Church, which is what we mean when we discuss the "invisible" church.
Only those invited by Christ and indwelled by the Holy Spirit are true Christians, and these are the Church exclusively. This group can be said to be invisible, because only God can know who they are with certainty. They are marked by the invisible Spirit of God.
On the other hand, the "visible" church is a term we use to refer to any gather of people in physical buildings under the banner of Christ. For example, when any Christian congregation gathers, it is a visible event (i.e., we can perceive it with our eyes), and so we call this gathering the visible church. Ideally, every gathering would consist entirely of true believers, in which case the visible church and the invisible would always be one and the same.
In reality, this is rarely the case, as many churches have unbelievers gathered unknowingly in their midst. Consequently, we use the term visible church to describe a union of both the true invisible Church (i.e., believers) with the false converts (i.e., unbelievers). This is where we would disagree with your comments. The visible church is a reality (not a fabrication), because it does exist as we've defined it. Real, physical buildings with real, living people do exist, and we call these gatherings the visible Church.
On the other hand, we are not saying that the visible church is comprised entirely of the true, invisible Church of believers. We acknowledge it is usually a mixed gathering of both believers and unbelievers. In the worst case, it is entirely unbelievers (as represented by the church of Laodicea in the book of Revelation), and in the best case it is entirely believers (as represented by the church of Philadelphia).
Whether any given visible church is "an abomination" to God is a matter of personal opinion, though the Bible does acknowledge the inevitability of unbelievers congregating with believers at times without suggesting it is an abomination (i.e., 1Cor 14:23; Luke 13:19, among others).