A persuasive essay is a piece of writing that describes a particular perspective and provides evidence in support of that perspective. While similar to an argumentative essay, the logic of a persuasive essay can be based on emotion rather than substantiated evidence, and it does not need to take the counter argument into account. Whether you are writing an essay for a composition class, or you are sending a letter to a newspaper editor, having a carefully crafted argument with solid evidence will make your writing more convincing and effective.
I think you might find this topic a little bit limiting because there aren’t very many reasons *not* to spay or neuter a pet. It’s not a debatable topic for most reasonable pet owners–the answer to topic 1, for most people, is a simple “yes.”. If your goal is to be debatable, you could push this topic even further by arguing that pet owners should be required to pay fines if they choose not to spay/neuter a pet (unless they’ve applied for a breeder’s permit or something). That’s one idea.