I agree with what you said about Apple products. I just can't help but disagree with your statement on Beats however. You're really just paying for the brand. The build quality on them is inferior to what you can find on a set of headphones a third of the price. Same for sound quality, I could never justify paying $300 for a set of headphones with at best, okay quality. This is something I'm hoping Apple will try and improve upon in the coming years.
^This. The problem isn't that Beats are expensive (in fact, ask any audiophile and $300 would be at the low end of the price spectrum for a good set of headphones). The problem is that they are expensive for what you get. Both audio and build quality are generally quite bad on most Beats (Studio and Solo lines).
I was really quite surprised when it was announced Apple would be acquiring Beats. On the one hand, both companies are similar in that they are very good at marketing their products to a wide audience. But Beats has none of the innovation and gravitas that made Apple the company it is today. I am very interested in what direction Apple will take Beats in in the future.
But in regards to why I buy Apple products (and iPhones in particular), the best way to sum it up is that Apple focuses on the big picture. Android phones are always touting their individual features, like larger screens or faster GPUs.
But at the end of the day, what matters for a device like smartphone that you use on a nearly constant basis is user experience. Apple has been constantly criticized for being "late to the game" or "playing catch-up" when it comes to implementing certain features (eg. cut-and-paste, 4G LTE, NFC, a display size on par with its competition). I don't see it that way. Apple didn't incorporate these features into their products because they weren't ready for prime time. When LTE came out, battery life was horrible for devices that had it. When NFC came out, very few devices had compatibility. An idea is no good if you botch the execution.
When it comes to software updates, it's always very cut and dry, and very predictable about what devices will get software updates, and which features each device will get. I would rather have Apple be straightforward about it than play guessing games with manufacturers and carriers of Android phones and then wait several months while someone else gets the update.
Build quality is also important. There are very few things people have on them at all times. This may be a wristwatch, a wallet, and of course a phone. There are definitely competitors to the iPhone that have build quality that is on par (eg. HTC One (M8), Sony Xperia Z3, et cetera), but you also have Samsung with its creaky plastic. I can see why that might appeal to some, but I like the reassuring heft of the iPhone.