She is being groomed to be dependent (I cannot cross a puddle myself, I need a boys help) and to be overly concerned with her appearance (I have to worry about my shoes getting dirty).
Let me ask you, do you ever think you would see a video of a little boy being carried by his older sister because the little boy is concerned about getting his shoes muddy?  Little children generally don’t care about concepts like getting their clothes muddy, because they don’t understand anything about cleaning, money, time, or effort with regards to clothing. Adults do understand this. Adults also understand that children are easily taught to depend on others and “learned helplessness” is taught to little girls a lot.
It’s also the phrasing used that inspired this reaction. I am an older sister, and I have several younger brothers. There were many times when my brothers were younger that they needed my help because I was older and bigger than them, and I could help them with things that they could not do on their own, because they were still children and too young to do it. However, this was never presented as me rescuing them, or being a knight in shining armor for them, or anything of the sort. The way it was typically phrase when I helped my siblings was that I was being maternal in some way. Isn’t that interesting? I wasn’t “rescuing” my brothers, I was “mothering” them, but this boy is not said to be “fathering” his sister, he is said to be “rescuing” her. Would we ever say he was “fathering” her? No, fathering usually means to have offspring, not to nurture, even though this boys actions are exactly like a father who is helping his child cross a puddle. That’s something to pay attention to as well.
The way I was raised is you help people that need your help, regardless of who they are, but you don’t infantilize anyone. It’s perfectly fine to teach an older sibling that as the older sibling, they should protect and help their younger sibling, but it’s very important not to present this as a gendered idea, because it shouldn’t be. Anyone who needs help should get help, and nobody should be infantilized and made to feel like they can’t do something or that they have to be overly dependent on other people.
The women talking on this post are women who have experienced being trained into learned helplessness, or being otherwise stereotyped, or taught to be overly concerned about our appearance. We are speaking from the experience of that little girl. No one gets to dismiss our opinions simply because you think this is just a cute video.
I have just a cute photo of a little boy kissing me on the lips when I was a toddler, because my parents thought it was cute to make me kiss little boys and make little boys kiss me.  These might be cute photos, but I can also look at those and say, well, that didn’t really teach me a good understanding of consent and boundaries, did it? And I can also understand that within the context of a society in which my boundaries as a female are constantly disregarded and disrespected. It might still be a cute photo, but it’s also a snapshot of a specific experience within a larger context that I can analyze and understand. 
