That a Ti frame is stronger is a gross simplification. Carbon is much more difficult to properly engineer and manufacture from raw carbon than Ti is from tubes (unless you are talking about the shaped and manipulated tubes like what Litespeed is doing these days), manufacturers have only recently gotten to the point where the engineering has caught up to the promise.
Much of the perception about carbon frames being fragile is left over from the days when they actually were fragile. Remember Vitus. But Ti has had its share of super fragile machines. So has Aluminium. The advantage of Ti is that it can be made without a fragile finishing coat, scratches can be buffed out, etc. So it can be more travel-friendly. But if you pack the bike properly, this should never be an issue.
Carbon is more vulnerable to puncture wounds than Ti, because the fibres aren't designed to support that type of load. But really, when was the last time you saw a frame get punctured? MAYBE on a mountain bike, but road??
As to the strength argument, one of the most highly stressed area of a bike is the fork. Think about it, there is no triangulation fore-aft. If carbon was so fragile, why is a carbon fork pretty much standard equipment on bikes of any material?
That you have been riding Ti, Al, Steel, or paper mache for the last 4 years is irrelevant to your next purchase.
Swimming Workout of the Day: Favourite Swim Sets: 2020 National Masters Champion - M50-54 - 50m Butterfly