I think the usual argument is that Ti lasts longer but carbon lasts for ages if you don't crash it and the people willing to spend $10k on a bike usually welcome the chance to buy a new one every 5-10 years anyway.
I'm not sure the argument that Ti lasts longer is really valid anymore.
I have 2 carbon mountain bikes that I've put thousands of miles on. Both are about 7 years old at this point. Early carbon as a bit fragile, but newer carbon seems pretty damned solid.
Even if you do break them, they are repairable. My wife broke the frame on her bike not long ago and she wound up getting it repaired. It was surprisingly affordable and the fix is likely stronger than the original.
The argument is not always true though. Welding of titanium is not easy, and often there is tension in the frame. Even 10 years and 50 thousand kms later it can crack. The better welding culture is in the US and Russia, but even then there are series of bicycles that earn a bad reputation for cracking.
Another argument against titanium is that mining and purifying of titanium is not so easy on the environment. If that is important to someone, it might get counted as a factor.
When 99% of modern Ti bikes have a carbon fork I don't think this argument holds up much. The advantage of Ti for me is that it is a metal bike (metal wears beautifully) without the weight penalty of steel. The downside is the cost...
Out of legitimate curiosity: what is the actual weight difference between a nice steel frame and a Ti frame? My nice road bike is 40 or 50 years old Reynolds 531 and it feels like it weighs nothing, especially compared to my mountain bike or my beater road bike.
My understanding is that with advances across the industry, it's pretty easy to build a bike under the UCI minimum weight, which suggests that you could make the frame out of whatever is best for the application.
Some of the lightest road bikes out there are steel, in the ~14lb range.
You can get stupid light in Steel, Ti, Carbon, Aluminum, but once you're in the sub 16ish lb range, you're going to be going with superlight parts all around, as there's just not that much frame left to make light.
You can make a fully equipped (steel) randonneur at 20lbs, with fenders, rack, pump, generator, and lights. It's not cheap (~10k+ is my guess), but man is it a well crafted bike. With some care, I think that style bike can be done with common components and off-the-shelf frames in the 25lb range.
I'm a big fan of steel bikes, so don't take this the wrong way, but you cannot build a steel bike as light as a carbon one for any reasonable price or robustness. The most high end steel bikes will barely be competitive with mid-level carbon weight-wise. If you are optimizing for weight, carbon is the only way to go. However, there is more to a bike than just weight :)
If you're going for stupid light, there are compromises. Money and robustness are the first two things to go.
Rodriguez is advertising production steel bikes at the 14lb level: https://www.rodbikes.com/catalog/outlaw/outlaw-main.html Yeah, they're pricey. (10k) (That's production vs custom frame, meaning that they might have one off the rack in the right measurements, if not it's a couple of hundred to do a custom geo)
But superlight Carbon is going to be up there too, and it's going to use basically the same parts, +- bottom brackets and such. And frankly, I would trust superlight steel before I'd trust superlight carbon.
There are some pretty awesome Ti bikes as well, including custom 3d printed lugs, cranks, forks, stem, etc. They are in the same weight range, and IIRC 8kUKP.
If you're looking at commercial production, probably fair that carbon is going to be lighter. But the the people pushing the edges aren't limited to that.
I have 2 carbon mountain bikes that I've put thousands of miles on. Both are about 7 years old at this point. Early carbon as a bit fragile, but newer carbon seems pretty damned solid.
Even if you do break them, they are repairable. My wife broke the frame on her bike not long ago and she wound up getting it repaired. It was surprisingly affordable and the fix is likely stronger than the original.