A number of things can convince people that synthetics can harm engines or transmissions.
Some time ago, a man claimed he changed to synthetic oil, and it wrecked his motor. It was likely, based on his general tone, that his motor was going bad, so he decided to try synthetics, in the belief synthetics would save a previously poorly maintained motor. It went out anyway, so he concluded synthetics wrecked his motor. He was rather hostile about it.
The same thing happens on transmissions. When it starts acting up is not the time to suddenly get religion and expect your sins to be forgiven because you use synthetics.
And, yet as the one example shows, there can be problems in some cases. But, not because of synthetic, but because, as someone said, a wrong fluid was used.
I sort of believe that using natural oils and fluids, if changed often enough, will indeed give good service. My personal concern is I am convinced engines which have a sludging problem are more likely to run into problems with natural oil. Still, the mostly obsolete 3,000 mile oil change cycle can almost certainly evade sludging, for most drivers. (Except the 2 miles a day to work types.)
In my case, I have been using Mobil-1 oil and synthetic fluid for some time. I do extend the oil change after lab testing my oil at 8800 miles. That does not mean someone with a different driving pattern can go 8800 miles. But, every so often I drop three quarts of fluid and add three quarts of synthetic fluid, total cost is very low because I do it myself.
If you, OP, are happy with what you have been doing, then there may be no reason to change. If it ain't broke, don't fix it.
By the way, some people do not think synthetic oil is any good. We had a man who insisted that a placebo effect convinced people it was good. Hohohohahahaheeheehee.