If you really think about it, a lot of things we do are odd. Squeezing juice from a cow (which, by the way, contains a significant quantity of pus as so many dairy cows have chronic mastitis there have to be quotas for what percentage of pus is allowed) to feed your child is odd. This seems much more odd than allowing your child the nutrition designed for them and provided lovingly by their healthy mother. I'm not being anti-dairy or judging anyone for drinking cow's milk. My daughter drinks and enjoys "milk from a cow in a cup". However, I'm trying to point out that many practices common place in our society would be seen as disturbing to anyone who hadn't encountered them before.
It simply isn't true that older breastmilk is designed just for babies prior to solids. Breastmilk composition changes over time to best nourish the growing child, including providing antibodies and immune modulators a child can't get anywhere else. The article already posted is a fascinating read and explains that biologically, evolutionarily and anthropologically it is clear we are designed to be breastfed well into childhood. Just because we as a society have lost our way doesn't make those of us doing what comes naturally "odd".
Feeding a toddler is very different to feeding a newborn. My daughter goes to nursery while I am at work and certainly does not cry for my breast while she is there. A nursing 5 year old may only nurse once a day or less. They have the maturity to regulate their nursing by then.
I actually do understand where you're coming from. I couldn't understand why anyone would nurse a toddler until I started on this journey myself and started questioning mainstream parenting as it felt so unnatural. But even when I didn't understand it, I would never have judged as you did. We all try to do what is best for our children, and for many of us here that is full-term nursing. Supporting each other to feel empowered to make choices we are comfortable with should be our goal, not shooting others down who do something you personally wouldn't choose to.
OP- Congratulations on reaching 3 years! A wonderful achievement in the face of these hostile and ill-informed opinions.