"Calling Thunderbird nonfree lumps Thunderbird in with programs one isn't
permitted to inspect, modify, or share."
Sure; inspect, modify, or share reflects back on the four freedoms.
https://www.gnu.org/philosophy/free-sw.html
And, thinking on those four freedoms, a given person needs all four of them
for that person to have freedom with a particular program.
As we read in to the Free Software Definition we have "'Free software' does
not mean 'noncommercial'. A free program must be available for commercial
use, commercial development, and commercial distribution."
The FSF explains why Thunderbird falls short on the "share" part of the
freedoms: One isn't allowed to share Thunderbird. At least, not fully in the
way that the FSF would want (to share exact copies both commercially and
non-commercially, given the comment in the Free Software Definition about
free software does not mean noncommercial.) Sharing copies both commercially
and noncommercially would be part of freedom #2. So it could be said that you
either don't get freedom #2 (since you can't share it commercially) or that
you only get half of freedom 2 (since you can share it non-commercially.)
So you only providing 3 or 3.5 of the 4 freedoms, depending on how you count.
Yes, there may be other programs that fall even shorter of providing all four
freedoms. Maybe they'd only provide 2 or 1 of the freedoms (or maybe even
none at all.) But does it matter how far they fall short of providing all
four? Whether it provides 1, 2, 3 or 3.5 freedoms, it's still less than 4.
What else does one call a program that provides less than all four freedoms?
"Non-free" is a common term. "Proprietary" is another.