My doctrine adds up just fine. You just remain naive to the fact that it's not hard to make believers mixed in with genuine believers in just about any group of "professing" believers. We saw this with Judas Iscariot and the 11 remaining disciples in John 15, yet the faith of Judas was spurious and he was an unbelieving, unclean devil who betrayed Jesus. (John 6:64-71; 13:10-11)
We also see this in 1 John 2:19, in which we read - They went out from us, but they were not of us; for if they had been of us, they would have continued with us; but they went out that they might be made manifest, that none of them were of us. Did you see that? 1 John 2 is addressed to "My little children" (believers) but as you can see, not everyone in this group is a genuine believer. You can also see that IF THEY HAD BEEN OF US, THEY WOULD HAVE CONTINUED WITH US.