The first, and perhaps the most important, reason for banning experiments on animals is because I believe it is wrong! Just as animals are simply different species, humans are a species, so humans are simply a type of animal. There's no mythical divide between humans and animals, humans are animals, albeit a lot more intelligent. If you can justify experimenting on one species, why not others? Such as the human species? For a start you are likely to get more reliable answers.
We feel we have a responsibility for other humans if they are in distress. This is because we have empathy with them. We know, from experience ourselves, that they may be going through pain, frustration, fear, and suffering. That is why we have laws to protect other humans, because we recognise despite any differences of gender, of age, of skin colour, of birth place, or beleifs, or any other irrelevant differences, that they desrve protection. Why should we not protect animals equally, on the basis that they have a right to life without pain?
Of course this does not mean we should give them the vote, just as, whatever you viewpoint is, you would not talk of giving men the right to have an abortion. Also, just because animals are incapable of having duties in human society, does not mean they can't have rights. Do children have duties? Do they have rights?
Us being the dominant species on the planet at this time is also no argument for the abuse of other animals. What people consider a "humane" quality is the wish to help the vulnerable. A "might is right" attitude surely isn't humane.
But we don't have to put animals before humans. I heard on a pro-vivisection video a hypothetical situation of a burning house with in one room each, a child, a beagle, and a Van Gogh painting. Who would you save? I'd say the human for the same reasons I'd save my daughter before a stranger. I imagine there's some people who'd save the painting first! Notice how they're trying to portray animals as objects, comparing a dog to a Van Gogh painting.
But all this is irrelevant: animal experiments are unreliable to the extreme. For example, penicillin kills guinea pigs, hamsters and cats, aspirin kills cats and causes birth deformities in rats, cats and dogs, and morphine sedates humans but excites cats, goats, and horses. Chloroform kills dogs. Digitalis raises the blood pressure in dogs to dangerously high levels, but not in humans. Also insulin causes birth defects in rabbits and mice.
The more tragic examples are the drug disasters. Thalidomide caused birth defects in humans, some rabbit breeds, and 7 primate species, but it was harmless in 10 rat strains, 15 mouse strains, 11 rabbit breeds, 2 dog breeds, 3 hamster strains and 8 species of monkey. Eraldin (practolol) was another example. In humans it caused blindness, death, and an unusual form of sclerosing peritonitis. Flosint shown "excellent tolerability" in rats and was "well tolerated in the dog and monkey", but not so well tolerated in the human, with 8 deaths and 217 "adverse reactions".
Prof. David Salsburg of Pfizer found in a lifetime feeding study in mice and rats had a less than 50% chance of predicting carcinogens in humans. He said he would have been better off tossing a coin. With results like that, lets ban vivisection because any method of testing is better than that.
Also see "The researchers dilemma"