Why isn't my mac book pro allowing me update to big sur? I backed up my MacBook (i can't find what year) and then deleted photos, which created 40 gb in hard drive. However, it still says I do not have enough space. What is going on?

I believe I have a 2013, but it does not say anywhere.

Well, the year is everything. Please do "About this Mac" from you Apple menu and find the SUB-MODEL:

Should be a similar window for Catalina.

Also see: If you can’t install macOS Big Sur on certain 13-inch MacBook Pro computers from 2013 and 2014 - Apple Support

Note that problems with Big Sur in some models caused Apple to block Big Sur downloads to 2013 and 2014 MacBook Pros for a while. I do not know if those issues were fixed and the blocks lifted. You may have to call Apple support for a definitive answer

11,1 looks up to 13-in MacBook Pro late-2013 OR mid-2014 model.

Both are theoretically qualified to install and run Big Sur if enough storage is available to install.

That exact upgrade was temporarily blocked because of problems. The article on the subject was just updated today (11 Jan 2021):

If you can’t install macOS Big Sur on certain 13-inch MacBook Pro computers from 2013 and 2014 - Apple Support

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40GB may not be enough.

If upgrading from macOS Sierra or later, macOS Big Sur requires 35.5GB of available storage to upgrade. If upgrading from an earlier release, macOS Big Sur requires up to 44.5GB of available storage. To upgrade from OS X Mountain Lion, first upgrade to OS X El Capitan, then upgrade to macOS Big Sur.

How to upgrade to macOS Big Sur - Apple Support

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