“I’m sorry that your cat died,” does not mean that I killed your cat.
But, “I’m sorry that I stepped on your foot,” does mean that I stepped on your foot.
In creating connection and trying to make amends, we often get confused by the two kinds of ‘sorry’, and don’t apologize because we believe the problem wasn’t our fault.
“I’m sorry that you had to wait two hours while your car was being serviced.” That’s a valid sentence, even if it wasn’t your fault that the schedule was overfull.
“I’m sorry that you’re stranded here and you’re going to miss the big meeting. I know it was important,” is a useful thing to say even if you didn’t cause the snow storm.
“I’m sorry” can simply mean, “I see you.”