Is the 'ultimate' purpose of the sexual urge reproduction?

We exist BECAUSE of reproduction. We do not exist TO reproduce, or to do anything else for that matter.

If we exist to do anything, we exist to reproduce, or to assist others with some of our genes to reproduce.
If you contend that we don’t exist to do anything, then your OP is kind of pointless. I can see the position, but if you wanted to talk about it you could have just said so.

Actually, kinda, we do. The reproductive instinct is powerful in humanity. It’s a really big part of how we’re built.

We also exist to fight: aggression is a really big element of our instinctive make-up. No human society has ever existed in absolute peace: at some point, some of the guys are going to get into a shoving match.

Lucky us, we’re smart enough to reason out ways around some of this instinctual baggage, but that doesn’t contradict the facts: we’re fightin’, fuckin’, and occasionally figurin’ beings.

People do eat for fun or to relieve stress. Eating releases happy hormines in your brain, which could be described as fun. To the extent that avoiding hunger is fun you could say everyone eats for fun. As a result of our intelligence, unlike other animals, humans can go on a hunger strike or avoid certain foods out of health or ethical concerns. You could draw analogies from these to differences in human/animal sexual behavior.

Think of the sexual equivalent of hunger and reframe the question. Do people masturbate for fun, or because they’re horny? Do animals have sex for fun, or because they’re horny? To me that would be some fine hair splitting, unless you believe mammals are robots lacking subjective inner lives.

So if women were only sexually receptive during limited windows and showed no interest in sex otherwise you’d say humans don’t have sex for fun?

inb4 wife joke

They would both be, if the second one wasn’t posted by someone who thinks that it refutes the first.

The first is an explanation of why sexual desire exists, namely that it’s been evolutionary beneficial and has lead to more reproduction than the opposite.

The second is an attempt at discussing the philosohical nature of desire, will and purpose, and not a particularly good one.

Now let’s have a discussion of which is the better fruit, apples or oranges.

Purpose is subjective and exists within the minds of individuals, but there is no unequivocal law within the universe that says that we must reproduce or continue the species or do anything else.

This is a valid point, but i think there are two critical differences in this situation

Firstly, i don’t think anyone would argue that somewhere in the brain of a giraffe is a thought about the future evolutionary path of its species. But absolutely there are many people who believe there’s an actual thought in the subconscious about reproducing. Clarity helps avoid this misconception.

Secondly from a philosophical POV many people believe our purpose is to reproduce. This belief is based on the misconception above tied with others such as conflating different meanings of the word “purpose”. Again the slight shorthand of saying we do X to try to reproduce is just not with the citizen here IMO.

I have no idea what prompts them to do it but they will not kill the cubs they sired (not sure how they understand the difference between their cubs and not their cubs). They kill only the cubs sired by the previous male.

The reason I have read was it would allow the females in the pride to start ovulating again (get into heat and be fertile) before they otherwise would (apparently while they are nursing cubs their reproductive system goes on hold or something).

I doubt the male lions understand any of that but they evolved to reproduce at every opportunity and killing the cubs aided in that goal.

Purpose is just a short hand for what evolution selects for.
There are lots of things which don’t reproduce - rocks, water, air. But the moment the first molecule that is self-replicating shows up, molecules that are better at self-replicating will dominate the environment. And we’re just a collection of molecules very good at self-replicating. While there is no purpose in the origin of self-replication, or evolution, there might as well be a purpose of replicating more effectively since the results are identical.