Because we believe in the rights of property owners.
But that's a pretty overstated response -- the sort of thing the anti- folks would say to mislead the public.
Texas property owners -- and ALL property owners everywhere -- have the right to restrict folks carrying guns and pretty much (almost) anybody else from entering their property. The same trespass laws that protect a property owner from having to allow someone with an offensive t-shirt or sign from entering their property, or someone not wearing shoes, or a panhandler, or someone who's making a ruckus, protects them from having to allow someone carrying a firearm.
Nothing has changed about that, either way, due to the relaxing of carry laws or the imposition of these signs.
The only thing that's changed is whether the STATE gets involved and levies criminal penalties on someone for what is merely violating a private party's policy.
I guess you could say that's a pretty extreme form of "protecting property rights" but I'd say we should think VERY carefully about how much we laud inviting the state to enforce BY LAW the policies of any private person or property owner.
Consider an analogy: Your neighbor put up a sign in your yard that says "No Cows Allowed." The next day your cow gets out of the fence and wanders across his yard on the way down to the local watering hole. Would you want the state to come and arrest you for violating his policy?
Now absent any law about the state enforcing "no cows" signs, he could simply come and tell you to get your cow off his yard, and that would be perfectly legal for him to do and you'd open yourself up to legal consequences if you refused. And, he could always sue you for any actual damage your cow did to his property while there.
But would you be ok with the state locking you up, or levying a misdemeanor criminal sentence on you for violating your neighbor's personal policy?
I certainly hope not, and I hope that adds some much needed clarity to the picture of what's going on in TX and other states where signs have the force of legal penalties.