Because 'user' wasn't in any way synonymous with 'customer', if it's in an organization then the organization itself might be the 'customer', but all the people who use it (in that org and everyone else who ever accesses/makes that copy) are 'users'; also, because licenses expire and PC software copying was rife back in the 1980s/1990s, so it was quite common that many of the 'users' aren't 'customers', or never had been.

Yes there is some objective history and reasoning behind this:

1. The analogies to hardware aren't valid (CD, VCR, game consoles, etc., or cars). You can't duplicate hardware (well not easily), and typically there is one customer and that person is also the user. This is self-evidently not the case with software.
2. As to Facebook and Twitter 'users', they aren't 'customers', they don't pay any licensing fee, so they can't have damages, and IIUC since there isn't any 'consideration' (money or other thing of value) they don't even have a contract with FB (IANAL); (they have a 'user agreement', but that's different, its terms mutate constantly, and it's very one-sided). Facebook's actual 'customers' are the people/companies who sell advertising on it, and/or pay or have licensing agreements for access to its datastream. Hence the adage: If you're not the customer, you're the product".
3. It was quite common that many of the 'users' weren't 'customers'. PC software copying was rife back in the 1980s/1990s (before US and other countries passed laws on DRM, and mandated building copy-protection/detection for content into the OS (Windows) itself and hardware (blocking or fuzzing the display of non-DRM content); there used to only be more basic software copy-protection, serial-port hardware dongles, and challenges to see if you owned the user manual ("What is the second word of the fifth sentence on page 208?"). Another anecdote: AutoCAD, the most widely-used(/pirated) CAD suite, was said to only have 7 valid (= purchased) license keys in all of Russia in the early 90s.
4. Even in a organization (or group) which had legit bought(/"licensed") the software, the 'customer' is the organization itself (or in a group, the individual who purchased it and allows other people access to it). There would be many 'users' but typically at most only one 'customer'.

Update: If, as many suggest, the term User originated because it was an early and specific role, what did that role originally convey in terms of the person's competence, privileges, or restrictions regarding the machine? And does the same role definition thus roughly translate into similar expectations for a customer purchasing an early micro-computer for the home or office?

This is tantamount to asking for an overview essay on the legal history of ownership in software, hardware and content (EULAs, shrinkwrap, DRM...), across multiple decades and jurisdictions, 1980s-current(!) That's a multi-semester course.

Because 'user' wasn't in any way synonymous with 'customer', if it's in an organization then the organization itself might be the 'customer', but all the people who use it (in that org and everyone else who ever accesses/makes that copy) are 'users'; also, because licenses expire and PC software copying was rife back in the 1980s/1990s, so it was quite common that many of the 'users' aren't 'customers', or never had been.

Yes there is some objective history and reasoning behind this:

1. The analogies to hardware aren't valid (CD, VCR, game consoles, etc., or cars). You can't duplicate hardware (well not easily), and typically there is one customer and that person is also the user. This is self-evidently not the case with software.
2. As to Facebook and Twitter 'users', they aren't 'customers', they don't pay any licensing fee, so they can't have damages, and IIUC since there isn't any 'consideration' (money or other thing of value) they don't even have a contract with FB (IANAL); (they have a 'user agreement', but that's different, its terms mutate constantly, and it's very one-sided). Facebook's actual 'customers' are the people/companies who sell advertising on it, and/or pay or have licensing agreements for access to its datastream. Hence the adage: If you're not the customer, you're the product".
3. It was quite common that many of the 'users' weren't 'customers'. PC software copying was rife back in the 1980s/1990s (before US and other countries passed laws on DRM, and mandated building copy-protection/detection for content into the OS (Windows) itself and hardware (blocking or fuzzing the display of non-DRM content); there used to only be more basic software copy-protection, serial-port hardware dongles, and challenges to see if you owned the user manual ("What is the second word of the fifth sentence on page 208?"). Another anecdote: AutoCAD, the most widely-used(/pirated) CAD suite, was said to only have 7 valid (= purchased) license keys in all of Russia in the early 90s.
4. Even in a organization (or group) which had legit bought(/"licensed") the software, the 'customer' is the organization itself (or in a group, the individual who purchased it and allows other people access to it). There would be many 'users' but typically at most only one 'customer'.

Update: If, as many suggest, the term User originated because it was an early and specific role, what did that role originally convey in terms of the person's competence, privileges, or restrictions regarding the machine? And does the same role definition thus roughly translate into similar expectations for a customer purchasing an early micro-computer for the home or office?

This is tantamount to asking for an overview essay on the legal history of ownership(/licensing) in software, hardware and content (EULAs, shrinkwrap, DRM...), across multiple decades and jurisdictions, 1980s-current(!) That's a multi-semester course.