For those who've said they can't imagine breastfeeding their toddler, of course they can't!
Nobody's asking you to suddenly feed an older child, but if you've done it from when they're a baby (which, of course you will have done), you don't see them as "suddenly" three years old or whatever.
If someone had handed me a 15mo child to breastfeed when DS was a month old, I'd have said "Er, no thanks!" But 14 months later, it's a different story. I can't imagine feeding him when he's two, or three, or four, but if he still wants it and I'm in a position to offer, whyever not?
And if it turns people's stomachs, they can just fuck off.