I believe the most two popular pets one can have are either a dog or a cat. In Germany, one must pay for tax when owning a dog (Hundesteuer). However a similar tax doesn't exist for cats, why?
The history of dog taxes in Germany is mixed and it predates German unification. Some principalities had financial motives, others wanted to discourage dog ownership (e.g. to curb rabies) without an outright ban.
There is a general perception that dogs are more messy than cats. While any owner of a garden can attest to the cat problems, even more people know the experience of stepping into dog excrement on the sidewalk or being accosted by a dog on a too-long leash. This has gotten better with recent regulations, which require dog walkers to bag and dispose of excrement, but that does not remove all traces. And the perception lingers on.
The discouragement factor has resurfaced, too, with higher taxes in some states on breeds deemed dangerous. Again, a complete ban would be politically difficult, so dog owners are steered to less aggressive breeds.
I am not aware specific situation in Germany.
In general I think it's simply because domestic dogs encroach on public space more than domestic cats. I've never noticed cat feces on the street or people walking cats very often. There are sometimes even designated areas for dogs in parks or poop bags by the trash cans, so it's natural that their ownership is taxed more when it costs us all something to build this dog infrastructure.
In the Czech Republic, the situation is such that individual municipalities can set a yearly dog fee. So that in big cities such as Prague or Brno, owning a dog is usually more expensive than in smaller municipalities. There is no cat fee as well as in Germany.
It seems to be a mix of history and practicalities.
German Wikipedia informs us that dog taxes were introduced some 200 years ago to discourage dog keeping, either to try to contain the spread of rabies, or to make attacks on humans less likely (also people who could afford taxes could afford to pay damages). Friedrich Wilhelm III. introduced a luxury tax on pet dogs, under the assumption that somebody who could afford to feed a useless pet could also afford to feed the kings table (working dogs were exempt from taxes).
Not all of this even applies to cats - cats feed themselves, and they do not maim or kill people (or if they do, they do it discreetly, and do not leave witnesses).
Cats do spread rabies, but as far as I can tell the solution for cats was not to tax them, but to kill them. I did not find an official law to that effect, but the fact that in 1927 Wilhelm Speyer could write a very successful young adult novel ("Der Kampf der Tertia") about students opposing a state ordered cat extinction event suggests that nobody found the premise particularly unusual (it was even adapted into a 1928 silent movie).
While dog taxes go into the large bucket that finances public works, they do not directly cover any costs caused by dogs. That is just not how taxes work, at least in Germany - determining how money is spend is the prerogative of the (local, in the case) legislature which creates yearly budgets. Setting a purpose for a tax would infringe on their rights, as well as create unwanted side effects (if government want to cover actual costs it has to levy a fee instead of creating a tax, which must not exceed the actual cost being covered. That in turn might set unwanted examples, e.g. if car taxes had to cover the cost of traffic nobody would be able to afford a car anymore). Dog taxes are what is called an "Aufwandssteuer", i.e. if you have enough disposable income to pay for unnecessary things, the government feels entitled to extract some of that (the general idea is that your good income is made possible because of the public infrastructure that is paid for by taxes, although people have been known for having more cynical views).
Instead, taxes are meant to encourage or discourage specific behaviour. That is the reason that there is actually a lobby to introduce cat taxes. For example hunters, at least the ones I know, hate cats with a passion - if you have a hunting lease in Germany, you need to ensure a certain population of live stock, which is difficult and expensive if cats go through the poultry. Hunters kill thousand of cats yearly, but that does not even begin to make a dent into their general population. Also conservationists would like to see less cats for vaguely similar reasons. But that is where the practicalities start.
For one, it is easier to raise an existing tax than introducing a new one.
Second, there are basically no stray dogs in Germany; locating the responsible tax subject for a dog is mostly a matter of looking at the opposite end of a leash. Cats however are incurably given to rove, which apart from all other problems provides cat owners with plausible deniability.
So in the end, cats are not taxed in Germany for the same reason guns are barely controlled in the USA - historically it is not something that was being done, a lot of people oppose it, and by now we simply seem to have missed the right point in time to do it. That does not mean it is impossible in the future, and some people are actively lobbying for it, it just means that for most politicians this is not the hill they want to die on.
Why is there no guinea pig tax? Canary tax? Two reasons:
- Enforcement. Dogs need frequent walks outdoors, if only to relieve themselves, they are day active, and are big and loud enough to be noticed. Therefore checks are easy, and because they typically need to be accompanied, their owner or somebody with ties to them is readily available. None of that is the case for cats.
- The need to regulate dogs, and the expenses they cause as opposed to other pets, become apparent when you compare the experience of stepping in their respective feces.