Honestly I think this is the best attitude to take! Who cares what other people think, you don't need to convince everyone and some people have some very strange ideas about breastfeeding full stop.
For example someone said Breastfeeding feels like something which should happen with small non-mobile babies - and I think that's exactly where it all stems from, all this cultural attitude, it's because breastfeeding is very much seen as something that's for tiny babies, maybe up to about 6 months max.
That's likely just down to cultural norms and what you're familiar with. It's not really based in any logic at all. It's "feels like it should" - which is generally based on things that we've always known throughout our lifetime (perhaps going back a generation or two because we will be influenced by our parents and grandparents' experience too).
If you went right right back much further than this it would be seen as completely bizarre - babies don't switch totally to food at a few months old after all. What you can actually trace this cultural norm to is the marketing of formula and baby food products. Even current marketing strives to promote the message that breastfeeding is for under 6 months, maybe maximum to a year, but after that you should be "moving onto" formula and bottles and solid foods.
My grandmother was told "you don't want to do that" and had her breasts bound up in hospital to prevent her from making milk. It was seen as better to use formula, and that is entirely down to marketing, formula was not originally created to replace breastfeeding, it was created to replace the crude mixtures that people used to feed babies with when breastfeeding was not possible (often with disastrous results). Then the companies just got greedy - wanting to increase their potential profits they started to expand into new markets, which is where breastfeeding starts to be targeted. The marketing is less overt now, but it's still there creating subtle hints all the time and the legacy of my grandma's generation and their experiences is still lingering too.
If you see breastfeeding as something which is only for tiny babies then yes, of course it would be infantilising and strange to feed an older child. That's why you get all these pseudo-psychological explanations like "it's sexual" and "the mother wants her child to remain a baby" or "it's attention seeking". But if you see breastfeeding as a totally normal part of early childhood, then most of these arguments simply disappear because they aren't relevant any more.
Logic, history, biology, anthropology, the behaviour of other mammals and the balance of potential harms all suggest that "a normal part of early childhood" is the correct answer. If you do think it's "only for tiny babies" then it might be interesting to examine why - usually, you'll end up in a circular explanation which is basically "I don't know, it just is" or "it feels like the right answer" or "everyone knows that, it's just a few weirdos who think otherwise", and that's a very clear sign that it's something that has been learned as a cultural norm, rather than making logical sense.
Nobody is blind to cultural norms BTW - I'm sure that I hold some beliefs that come from them too. But I think it's always an interesting premise to examine a belief - why is this true, could anything else be true? What assumption is that based on, could that be untrue?