Well since you asked, and no one ever seems to have any qualms about slagging off where I live - part of what I love about London is that it is quite different from the rest of the country - socially, politically, culturally, economically. Although there are a lot of threads saying how awful London is, there are also a lot saying those there Londoners don't know what real life is like, with their cushy jobs and cushy public services. We have a lot of immigration, obviously, but funnily enough the majority of Londoners are totally OK with that. I sometimes feel I live in a bubble sheltered from "real life" but, frankly, it's quite cosy in my bubble. I like that my neighbours are a diverse, open-minded, well educated, generally rather left-wing bunch. I like that I don't need to worry about not fitting in like I did in my Northern town. I can just be me, and there are enough people to go around that I slot in and find my niche.
I like that I can get up on a Saturday with no plans and by the end of the day have visited a world class exhibition or a national museum, or just wandered along the South Bank looking at landmarks. Yes you could visit if you lived further away, but it's not the same as being able to pop to a gallery during your lunch break, pop to the South Bank after school, just take advantage of the variety of a city that's ever changing and always offering something new. I've lived here for 15 years but there are still places on my "to do" list.
Also, of course most jobs exist to a certain extent outside London - but if you want your pick of the best jobs, be it in the field of the arts, Government, financial services, then London is the best place to be. You can find not just "a job" but your pick of jobs, and when you get bored of that one there's another load to choose from. London=freedom, and attracts people for whom that's attractive. It makes it an exciting place to be - and people that I meet tend to be interesting.
And actually life here isn't so hellish, even measured against the things you might value about the suburbs. I have a house with a garden. My kids are at an outstanding primary school 5 mins walk away. Their friends all live within walking distance too. I have a view of trees, loads of parks within walking distance, Hampstead Heath a bit further away. My commute to work takes 35-40 mins but 15-20 mins of that is walking through the park.
I realise this isn't everyone's London but it's my London and you asked me why I live here. I accept I was lucky - I bought my first flat in London and my house is now worth a lot of money - that brings freedoms too and I owe that to London.
I do worry that my London might not be on offer to the next generation but am hopeful it may be. It somehow does continue to open itself up. Where I live isn't the fanciest. It was downright rough not that long ago - but generally if you're open minded and don't run away from the less attractive bits of life, you can find a pocket of London to call your own that grows with you.