I would have to confine Willie inside to expose them to each other
inside,
otherwise he would simply run outside at first sight of Thug. Willie
has
never been confined inside. He has always been free to go in and out
as he
pleases. I don't let the cats in and out. They always have a way to
go
in and out without having to ask.

Of course I could confine him, but it would be like a betrayal of his
trust

This just appeared on my reader so.....

I had assumed that Willie spent a certain amount of time in the house
with the door closed - didn't realize he was a 24/7 outdoor cat. Mine
come inside at night and stay inside till morning.

I can see why you're having a problem - neither wants another adult
male cat around and you don't have much control over their
environment. Basically, you can't force them to deal with each other
until they arrive at a detente unless you're in a controlled
environment. The point of an introduction is that neither cat *can*
drive the other cat away, as much as they'd like to. If they actually
*can* drive the other cat away from the house, then there isn't much
incentive to work things out and they won't.

You have to decide if keeping Thug is worth putting Willie through the
introduction process - INSIDE. You do it as kindly as you can, but
there really isn't any other way. It isn't going to happen outside and
Willie runs risks if he is driven too far from his familiar territory.
Yes, it's hard to confine a cat who isn't used to it, but things have
changed, and for the longterm health and survival of both cats, it
would certainly be better if they could learn to tolerate each other.
I don't think it's impossible, but it will take alot of time and
probably a fair bit of discomfort for Willie and for you. I wish there
was a better answer, but I don't see how else it can be done.