I did extended breastfeeding and noticed this sharp dropoff in acceptability at 1yr old (exactly, not "around 1").
I put it down to 3 things. Cows milk, work and TTC.
12 months is the recommended age for cows milk being acceptable for bottles etc. So most people believe that cows milk is as good as breastmilk, so no point to breastfeeding. This belief is mistaken, there are many benefits in continuing to breastfeed, as the WHO has taken into consideration in their 2yr recommendation.
Secondly, many mums are heading back to work at 12months, having used up maternity allowances, annual leave etc. So having the baby on cows milk or formula is much less stressful when negotiating childcare etc. Of course older babies don't often need milk as often during the day, so many mums heading back to work could express one feed for the childminder and not miss that closeness and bond they have with breastfeeding - after being away from baby part of the day, I would have thought snuggles and breastfeed together would be bliss for both mum and bub.
And some friends stopped at 12m because they wanted their cycle back to conceive the next child.
Many people shy away from the concept of breastfeeding infants with teeth and/or speech. The idea that babies could ask for boobies seems to freak people out.
For me, they were still my baby when they turned 1 - there was no day I decided that I needed to stop breastfeeding because they were too big for it. If you'd told me I'd breastfeed my children until nearly 3yrs I'd tell you that was bonkers, I was a professional woman, who had no lurking hippie gene in her body. Alas, it isn't a hippie gene, but a happening of circumstance, my first was very sick at 1yr old and weaning him when he was very ill seemed wrong on many levels, at least he was getting the food he needed in a digestable form, as well as comfort when he felt lousy. Then by the time he was fully recovered, I guess I had realised there was no reason to stop until he was ready to.