Why shouldn't you pay for half the total costs?

Well, for one reason, people who rode with me in my airplane, over the
past 30 years, on trips to Alaska and other places, shared operating
costs, not hangar rent, insurance, or opportunity cost on my
ivestment. (I also didn't ask them to pay half the cost of my
aviation medical exam! Or half the cost of getting my licence, 50-some
years ago! How about that!!! Am I generous, or what???)

For another reason, that's what the FAA appoves, if I read the FARs
correctly.

If your friend hadn't invested in the aircraft then you would have to rent one.

And if I hadn't agreed to fly with him, he would have had to pay the
full operating cost of the trip, instead of only half of it.

How is it fair that you should only pay for fuel direct cost?

You should read posts carefully before replying. I explicitly said
that I would pay half of full operating costs, not "fuel only."

vince norris