what is the problem with a late 2013 27 inch imac downloading and installing big sur

that the mac does not meet the big sur requirements

macOS Big Sur - Apple

See if your Mac can run macOS Big Sur.

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iMac

2014 and later

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MacBook Air

2013 and later

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iMac Pro

2017 and later

(all models)

MacBook Pro

Late 2013 and later

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Mac Pro

2013 and later

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MacBook

2015 and later

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Mac mini

2014 and later

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it's because it didn't make the cutoff that apple decided. you need at least a 2014 iMac to be compatible with big sur. we are only fellow users in this forum. you would need to ask apple why the 2013 iMac can't run big sur.

Lack of proper hardware support, and the fact that the 2013 iMac is now on Apple's vintage and obsolete product list, another reason why it does not get current operating system support.