Boundaries exist between humans and animals in regards to medical testing, housing, ownership, euthanasia, purchased breeding, and a number of other areas, so why would it be different for cloning? A slippery slope would indicate that one could easily go from one position to another, taking a leap that standards for animal welfare are suitable for human welfare, but there are ethical, cultural, and mental boundaries that exist between animals and people that would keep what is done in animals from automatically becoming acceptable in humans.
Cloning is a method of reproduction, specifically asexual reproduction: the genetic contribution is from one individual. The human norm, and often the norm in animals, is sexual reproduction in which the genetics contribution is from two individuals. However, the use of cloning techniques and the reasons for attempting cloning fall across ethical boundaries. However, a similar ethical question is selective breeding - Is it unethical to selectively breed pets? In current practice the answer is no, but it is considered unethical to selectively breed humans. It is this same unslippery slope that exists for cloning.
There are, of course, exceptions with those who choose a partner based on physical characteristics they want their children to have, and those who select sperm donors based on stated characteristics or family disease history. The cloning of pets simply ensures the genetic result by using the pet of choice to produce a physically identical pet. This may be due to sentiment, or it may be due to breeding quality. Cloning a pet would not recreate the animal in its personality, memories, or habits - it simply reproduces the genetics of that animal in a manner similar to how nature reproduces animals. The difference is simply the number of genetic contributors. Is this truly unacceptable in humans? Maybe not, but there are different ethical questions to be addressed prior to the establishment of the technique that do not extend directly from using it with pets.
What determines the ethics of the use of cloning in people is the question of why people seek to clone themselves and how they are going about it. If a person is simply wanting to not have to deal with the unknowns of a partner's genetic contribution to have a child, is this really wrong? There are already single parents having children from in vitro fertilization (IVF) using sperm from unknown partners. Cloning is this same process, but with the use of an egg and two sets of genetic material, all from the same donor instead of from two, but it is the same exact zygote and embryonic process after these elements are combined. A clone is not any different from a natural born child, except its genetic outcome is known.
There are examples of unethical cloning in humans - organ harvesting being a prominent one. Would this be unethical in animals? No, because we already harvest animals for food. This is a huge difference to prevent an easy transition from animal to unethical human cloning.
We ascribe humans a superiority that we do not give to animals. This makes us willing to buy, sell, cage, eat, and breed animals, which we would never conceive of doing to humans. So it is not a slippery slope, and I would even go so far to say that cloning, in most cases, is benign and not unethical anyway.