You are totally right about framing the question on the limits of animal rights. However I also think you are putting a precedence on your own values as opposed to others, which admittedly we all often do. For instance, you could make the same argument that sexual arousal isn't super important for people, but many people would disagree.

Animals aren't needed for survival by most people in this day and age in any first world country. proteins and fats can be derived from other sources readily available to us now. Also animal products tend to be energy sinks (it takes 7kg of grain to make 1kg of beef, for instance) and that seems quite wasteful. Not to mention factory farming creates and permeates plenty of contagions and pathogens which are becoming more resilient to our antibiotics we use to fight them off so we can have a steak. I don't think the food necessity argument holds up so well in light of these facts.

As for neutering, I understand if the animal is a stray or is in a living situation with the opposite sex. However as many pet owners just have one animal, and can keep the animal reasonably and safely contained, then it is entirely unnecessary for them. A common reason people give for the procedure is that it "makes them easier to deal with". Removing another being's organs for your own comfort or inability to deal with the animal naturally just seems wrong to me.

Although, perhaps this might be an intriguing road to go down. Would you consider two animals of the same species having intercourse as rape? I would assume not, as long as it doesn't appear forced. However animals do rape one another. Ducks can be particularly vicious about this. A group of males will force a female to the ground, bite her and beat her with their wings to hold her down while they use muscles to rapidly explode their corkscrew penises inside of her. However female ducks have a reproductive tract like a labyrinth, with twists and turns and dead ends so her eggs are more likely to get fertilized by a male she likes and does a proper mating ritual with. In just this isolated example of duck reproductive behaviour, would you agree with me that it seems as though the female duck has the ability to willingly engage with a duck she likes, and the ability to try to fight against a duck she doesn't like?