Where does the bible say this?
Matthew 24 clearly says the trump sounds "AFTER the tribulation of those days" and the elect are gathered at this time, NOT before.
My dear friend you have to see things thru the window of dispensationalism. This section is talking about the people who survive the tribulation period who are unsaved. The Angels of God will remove them and the 1000 year reign of Christ will begin. All surviving individuals who are regenerated -by Faith in Christ- will only enter into the Kingdom. Read Daniel 12:11-12, Matthew 13:29, 30, 38-43, 46-50. That which offends will be removed.
Also, the trumpet is not even mentioned in Matt 24. I once also held that view. I encourage you to look thru it carefully and be objective. It is always well to challenge your belief to see if it stands the Biblical test. I have always done it and Almighty God has always lead me to the truth. Here is alink below that might be helpful
God Bless! (John 16:12-15)
http://www.middletownbiblechurch.org/dispen/dispensa.htm