Nobody likes taxes. A few of my libertarian friends believe all taxes are immoral. Everybody else accepts that some government is necessary, and thus some taxation is legitimate. But some people really, really don't like property taxes (as witnessed in push back against Curtis Shelton's latest post), and I don't get it.
For my part, I subscribe to the Declaration of Independence argument. Human beings have equal unalienable rights that are the reason for government (and taxes), but also the reason why government (and taxes) must be limited. Those who signed the Declaration had no problem with taxation done in a legitimate way. Remember, they were against "taxation without representation," not just taxation in general.
Once we accept that some taxation is legitimate, there is still the question of which forms of taxation are better or worse. There seem to be two arguments against property taxes.
One is a moral argument, that property taxes mean you don't really own your property. This is really just a return to the general argument that all taxation is illegitimate. If taxing your property means you don't own it, then taxing your work means you don't own your labor. If this way of thinking is correct, income taxes are a form of slavery (again, I know some of my libertarian friends—and they really are friends—think this way, but I disagree).
A more practical-sounding variant of this argument is that if you don't pay your property taxes, you'll lose your home, and thus property taxes are uniquely bad. It's true, as far as it goes. But if a business owner fails to remit sales taxes, eventually the taxman will come for his property. And if anyone with significant income ignores the IRS for long enough, the feds will feel free to seize his property to pay the judgment.
The more compelling argument against property taxes, in my opinion, is even more practical: high property taxes push people out of their homes. This is especially true in areas where property values rapidly rise. But this is a reason to limit property tax rates and increases, and to have safety valves for people on fixed incomes, rather than an argument against any form of property taxes. After all, other taxes can get so high that they drive people into poverty or compel taxpayers to sell property to pay the bill.
All taxes are harmful. They are involuntary transactions, extractions by force. Just like everything else government does, they must be checked and balanced and limited and subject to transparency and oversight. But if we're going to have government, and thus taxation, we should think carefully about which taxes do the least harm.
Conservatives in particular should disfavor taxes that result in volatile swings in revenue. Those swings become a one-way ratchet. They drive the rapid growth of government in boom times, but government almost never shrinks in the inevitable downturns. Supporters of big government often successfully use downturns to argue for tax increases, which then amplify the next boom ... and bust.
All those who care about economic growth should disfavor taxes on production and investment. If we tax cigarettes to make people smoke less, why on earth would we tax work? Why would we tax someone on their investment in a business? We want as much work and investment as free people are willing to produce. Income taxes only make sense if the goal is to punish success, or to redistribute wealth. Otherwise, income taxes are dumb.
One of the least volatile taxes is the property tax. And while investments can increase property values leading to higher property taxes, still the property tax is not a direct tax on work or investment. Compared to income taxes, property taxes are a more stable and less damaging way to support legitimate government functions.