Was it working before you started messing with it? It would have been far better to note which wires went to which terminals of the switches and then identify the common terminal on the switch.

There's not enough information in your analysis to identify what exactly is going on. If I had to venture a guess, the two that are hot in the last step are the live traveller from the first switch and the common going to the light. What happens when you throw switch 2? I'd expect one of the lines to no longer be hot, that is likely the common.

Is there a problem? How is it behaving contrary to expectations?

yes it was...my son-in-law replaced a 3 way switch with another switch that wasn't 3 way and thinking the job was done, but without testing to ensure working properly, fininshed off the job. He did not mark the wires so as to enable what you indicate so I am trying to unravel this puzzle. I told him that he needs 3 way switches for what he was doing.

i am going to flip switch number 2 in both positions to see what is hot and what is not. I'll check that tonight. I think #1 is wired ok and that the problem is with #2.

Power to common on switch one.
Light to common on switch two.
IF switch one is correct then disconnect wires at switch two and check for power. Power on one wire is traveler, flip switch one and check for power at switch two, hot one is second traveler, remaining wire goes to common and light.