Summarise "How Feminism Is Stifling Our Sons."

Title is correct, but something to be aware of is that you will see American and Canadian English spell "summarise" as "summarize".

In her essay, "How Feminism Is Stifling Our Sons.", Carter noticed that young boys lack role models which is harmful for both boys and girls after the rise of feminism.

As Carter herself put it best, "Tthe vacuum is currently empty and the chances for toxic masculinity to pour inside are high."

Quotes in English inherit grammar and syntax from the sentence they are being used *in* and not the sentence they come *from*.

So even though "the" is the first word in the original sentence, you wouldn't capitalize it in the middle of your current sentence.

In other words, she demands forthat there be positive male representation tofor the young boys to follow.

"demands for" sounds a little unnatural in writing, but this is definitely something that would pass in spoken English. Made small modification to make it flow a little more naturally.

In her essay, "How Feminism Is Stifling Our Sons."," Carter noticed that young boys lack role models, which is harmful for both boys and girls after the rise of feminism.

Minor punctuation errors

In other words, she demands for positive male representation tofor the young boys to follow.

In other words, she demands for positive male representation to thefor young boys to follow.

Use 'for' instead of 'to'.
Unless talking about specific 'young boys', 'the' isn't needed :)