Breast Feeding Beyond Two

Would you really want to breast feed beyond a year let alone two. They are toddlers and eat normal food why do they need breast milk?

I breast fed Ollie until he was four months I would have for longer but my milk dried up as I also used formula because I was told he would sleep more at night - he didn't.
I'm still feeding Joel at 2 1/2 months and hope to continue but the thought of doing it beyond two years freaks me out, it would feel wrong to me.
On a post I read earlier on Facebook, women were continuing to breastfeed for 3 years and over..........utter madness they are so big at that age I don't understand it.

Is it me or does anyone else think this is odd?