If you go to https://openlibrary.org/, a search will turn up 52,223 interrogatives (questions) that begin with "Why cannot" in published English literature and there are over 2 million examples of interrogatives that begin with "Why cannot" on the internet.

Looking at a specific example, "Why cannot we" turns up with 758,000 interrogatives (and 8,064 examples in published literature). There are also many examples of "Why we cannot", but they are not interrogatives.

JForrest explains that 'cannot' is the negative form of 'can', and so 'cannot' should be placed in the same location as 'can' would be in a sentence. https://www.youtube.com/watch?v=55d1OSJ-dIk&t=303s Since we can say "Why can we grow taller?", "Why cannot we grow taller?" is a logical and properly written negative. We don't say "Why we can grow taller?" so the construct should not be "Why we cannot grow taller?" The reason is that auxiliaries should come before the subject to make an interrogative. (https://grammar.collinsdictionary.com/easy-learning/what-is-an-auxiliary-verb-in-english)

I argue that the "Why cannot" usage is acceptable because of that rule mentioned by Shinji, above, that "you can place one and only one auxiliary before the subject in an interrogative phrase". Thus, "Why cannot" is acceptible though "Why can not" is not.

I admit that some people argue that the contraction "can't" should be used instead in this case. That option is quite popular - there are 16.6 million examples of can't on google and 90,470 in published literature. It is much easier to type can't, and easier to speak it as well. Contractions generally aren't considered ideal for formal writing, however.

Another alternative that is growing in popularity is the construction "Why can we not" which sees 1.2 million uses online 9,900 in publication.

If you go to Open Library, a search will turn up 52,223 interrogatives (questions) that begin with "Why cannot" in published English literature and there are over 2 million examples of interrogatives that begin with "Why cannot" on the internet.

Looking at a specific example, "Why cannot we" turns up with 758,000 interrogatives (and 8,064 examples in published literature). There are also many examples of "Why we cannot", but they are not interrogatives.

JForrest explains that 'cannot' is the negative form of 'can', and so 'cannot' should be placed in the same location as 'can' would be in a sentence. Since we can say "Why can we grow taller?", "Why cannot we grow taller?" is a logical and properly written negative. We don't say "Why we can grow taller?" so the construct should not be "Why we cannot grow taller?" The reason is that auxiliaries should come before the subject to make an interrogative.

I argue that the "Why cannot" usage is acceptable because of that rule mentioned by Shinji, above, that "you can place one and only one auxiliary before the subject in an interrogative phrase". Thus, "Why cannot" is acceptable though "Why can not" is not.

I admit that some people argue that the contraction "can't" should be used instead in this case. That option is quite popular - there are 16.6 million examples of can't on google and 90,470 in published literature. It is much easier to type can't, and easier to speak it as well. Contractions generally aren't considered ideal for formal writing, however.

Another alternative that is growing in popularity is the construction "Why can we not" which sees 1.2 million uses online, 9,900 in publication.