Introductions have always been the hardest part.
I mean, sure he could grab their hand, tell them to run and then drag them outside before blowing up their work. And then of course have them be stalked by living plastic, save his life and then come with him on a whirlwind trip into time and space and then ... but he doesn’t want to dwell on that particular introduction.
But then again, he could not be doing the introducing. He could just find himself face to face with a screaming bride who was supposed to be getting married in a church in Chiswick, and not in his TARDIS spinning slowly around a burning up sun after using it to say goodbye to that certain person he'd rather not dwell on.
And then, he might just happen to be in the hospital that gets taken to the moon, invaded by rhinos and plasmavores and just nearly blown up. And then offer a once in a life time trip to someone who’d saved his life. And then practically destroy theirs.
This was why he didn’t travel with anyone.
Because, it was never sorry that’s the hardest word, no matter what people think. And it’s not goodbye, no matter what he may think.
It’s hello, which always leads to the sorry.
And almost inevitably, leads to the goodbye.