Where does he come from, where does he go to?

(is there a basement? crawl? below? attic above?)

after that it's a matter of importance like is it some unused thing from eons ago or what? / room available to move it further left, provided of course there's not another one we can't see or something else?

Yep, if you got the money... I got the time / solution. ( I like your attitude)

The con with finding buried treasure is you have to keep digging if you don't find anything -- the time spent removing obstacles in your way is yet another. Maybe they put that pipe there as a marker to the buried treasure just due left. (ha, ha, ha) The pipe looks awfully shiny? why?

I service the Katy, Texas area.

Can you tell me what the pipe is and if it’s recommended not to move it?

The pipe appears to be an HVAC supply duct. I assume the furnace or air handler is in the basement and this is one of the supplies for the second floor. If done correctly, moving it over into the next stud bay is not going to compromise the heating and cooling performance. During the move you have the opportunity to install a wider duct if needed.

If this is a load bearing wall then alterations become more complicated. It can be done it just increases the cost.

I’m no construction expert, but if your contractor doesn’t want to move it, that’s a red flag.

Either he knows what’s involved and believes it’s going to be a huge PITA, or he has no idea what‘s going on and knows he’s going to be in over his head.

As Mike said, or it could be a ducted return, maybe even a dryer vent (we only have 1 pic and no other info to go on). But typically, you map out what is above and below to understand what plumbing, electrical, mechanical, and structural implications you have prior to exploratory surgery. So once you open up, you already have an idea of what it will entail and some plan B's to continue, most of what you find will be confirmation. Otherwise, if what you see (prior to exploratory surgery) is too much beyond the project scope and budget, you might want to change the project design to work around it or change where you do the exploratory surgery.

For this spot, whether you open up the entire wall or not will play a part in what can happen.

We hired an hvac person to come and move a duct that was in the way. He did a great job and worth the expense.

Can you tell me what the pipe is

No, we cannot. You should be able to figure it out since you are in the house. It starts somewhere & it ends somewhere. Find either one of those ends & you will have answered your own question.

It is not unusual for a contractor to "not want to move" something. The reason is usually that it's more work. You have to ask "why not?" and also "so what is this anyway?".

"We hired an hvac person to come and move a duct that was in the way. He did a great job and worth the expense."

This is what you need to do.