Volitional: 見せましょう does not mean “let's have a look”?

Question

部下：すみません、部長。この書類、見ていただけませんか。
部長：
1. ご覧になってください。
2. 会議のあとならいいですよ。
3. すぐに見せましょう。

Source: Japanesetest4you

Option 1 means, "Please have a look," using the honorific equivalents of 見る and くれる. This does not fit the context.

Option 2 is the given answer, to which I have no objection. However, I feel that option 3 is also a viable choice, because 見せる means to show something. Saying 見せましょう seems to me like the 部長 is allowing the 部下 to show them the 書類. I think this can be thus translated into English: Let's have a look right away then!

If my understanding of this usage of the volitional form is correct, why is option 3 not correct?

どうぞよろしくお願いいたします！

Answer 1

見せましょう would literally translate to "Let's show it (to someone else)!"

So it's not something that a boss would say to a subordinate who is trying to ask them to look at something.

Possibly 見ましょう could be said by a boss at this point, though that seems a bit too relaxed a response, it would translate to "Let's look (at it) (together). However, since the subordinate is asking the boss to check something, in theory because his authority is needed, or his input is what is valued, there is little reason for him to suggest looking at it together with the subordinate.

Answer 2

～～ましょう (or ～う・よう in casual form) can mean either "I'll ~~" or "Let's ~~".

＃2 すぐに見せましょう would mean either "I'll show it to you right away" or "Let's show it to [someone else] right away", so it cannot be a correct response.

すぐに見ましょう can mean "I'll have a look at it right away", so this could be a correct response. It can also mean "Let's look at it (together) right away" depending on the context.