That's the big thing; when I express doubt about the worth of separating our rubbish into the recycling bins to my wife I get dirty looks at best!
"I feel OK, I recycle, it's the best we can do."
You have both done well to articulate that it doesn't feel right, but do you have any actual proof against the value of recycling? And I don't mean trade-offs, I acknowledge recycling isn't perfect, but there are plenty of statistics that prove it is worthwhile.
If you can't find them ... that would tell you something.