See is vidět, look is dívat se. Maybe see is an idiom, but it is not a correct translation of the Czech sentence. You can look and still see nothing (dívat se a stejně nic nevidět).
"vidět na vlastní oči" - "see with your own eyes" is also an idiom in Czech. But it simply means something else.
Why does it not work? Is the must a problem? It surely can't be just the looking. https://www.google.com/search?q=%22look%20with%20your%20own%20eyes%22&tbm=bks&lr=lang_en
I don't know how to interpret those charts, but when I entered 'see with your own eyes' compared to look, it found many more instances. Anyway, surely word-for-word translation is often inaccurate and not really the goal here. Otherwise wouldn't you have to accept translations like 'there are to me 40 years' when the sense is "I am forty years old"?
You must look with your own eyes. makes no sense because... How else can you look.. if not with your own eyes. (You have to see it with your own eyes ) means that " I can't describe it to you it is unbelievable you have to see it yourself!! " So if 'You have to see it yourself 'is not acceptable , then maybe a fellow English speaker can give me a situation in which I would use that 'must' expression, I can't think of any. Thanks Although you have to look with your own eyes. is acceptable. you have to see it with your own eyes is better.
No, the Czech sentence really says what the English "look" does. It does NOT mean that you have to see it with you own eyes because I cannot describe it. It is just a wrong translation.
It is just a poetic sentence, that's all. It can be used in the context of visual arts, e.g., by Gilbert Stuart http://www.arkellmuseum.org/content/look-your-own-eyes-landscapes-portraits-and-pastimes-american-paintings