John 3:16 and the 5 Points of Calvinism

It is commonly believed that any serious study of John 3:16 would force Calvinistic Christians to renounce the five points of Calvinism (the so-called "TULIP") and to believe them no more. The reasons for this are many. First, this verse seems to teach that God the Father loves all the human inhabitants of this world, but surely Calvinists don't believe that! They believe the verse should read "For God so loved the elect...", right?! Second, it is assumed by many that this verse teaches that Jesus Christ died a substitutionary death in the place of every individual inhabitant of the earth. But does this verse teach us anything about the extent of Christ's atonement? Or does it teach that Jesus Christ is an all-sufficient Savior who is able and willing to save any and every sinner who comes to Him repenting and believing? And is something that Calvinists deny? Third, this verse also seems to imply that the good news concerning Jesus Christ should be proclaimed to all men without discrimination, and that every sinner should be told of the free offer of eternal life in Christ Jesus. Indeed it does, and this is what Calvinists have believed and preached for centuries! If you are new to the doctrines of grace, or if you have been somewhat skeptical of them, this Bible study may surprise you! Belief in the Sovereign Grace of God should not stifle evangelistic zeal, it should PURIFY it!!!!! Indeed, it should serve as fuel for our confidence in evangelism, and it should help our witnessing to be much more God-centered than it presently is.