All you have to do to prove your claim is:

(1) provide a PERCENTAGE of the cats you've TNR'd.  You'll need to get to AT LEAST 80%-90% just to "stabilize the population"--the rate of increase is about one-third annually

(2) explain why, despite SIX DECADES of practicing TNR, the UK stray and feral cat population has more than DOUBLED from 4.1 million in 1965 to 9.1 million today.

(3) explain how sterilizing cats prevents them from contracting and transmitting toxoplasmosis.  I'll make that one easy for you--it doesn't.

(4) What was that you were saying about laughing at idiots?  Are you standing in front of a mirror?