Why do units insist that a SM wear the unit patch as the combat patch while deployed with that unit? I resist this.

Esprit de Corps. I have heard this one before. I found it wasn't a hill I was willing to die on. Oddly more common the closer one gets to the flagpole..

I was approached in Theater by a SGM from the 10th mountain division. He wanted to know why I as a SSG was not following the guidance put out, all were to wear the 10th patch. I let him know that I had 28 total months with the unit I was wearing. And lost 6 friends in that unit. As soon as the 10th CAB exceeded that I would continue wearing my patch. Granted I used more tact.
I know the reg so why are SGM making police where the reg is clear it is the SM choice

Don't forget that AR 670-1 is no longer the full story- it directs you to now the supplement DA Pam 670-1 to tell you how to wear the patch. Paragraph 21-17 specifically says soldiers authorized more than one have the option of choosing which to wear, or electing not to wear. On top of that, don't buy fully into the "local guidance can be more restrictive than the regs." The rule is the rule, and the role of local commanders policy is intended to implement the regs and fill in the gray areas. Here it says the soldiers can choose their own patch in black and white. I don't know what commander presumes to say he is going to take away your choice that is specifically authorized in the regs, but they don't have that power.

All that said, sometimes it's a matter of picking your battles...

Come and get it, Sergeant Major. Be sure to tell me how "your way" trumps Army Regulations.

I resisted that too. I wore a Combat Patch that I earned from a LRSC (Long Range Surveillance Unit) that had less than 160 people that wore it. So that I wore because it was different.

I irritated the MMB (and my Team Leader) in Iraq by not wearing the Med BDE patch that the MMB that we fell under wore instead wearing my unit patch. Team Leader said I had to wear the MMBs patch, and I responded with the regs...tactfully of course...she quieted down. The MMB CDR and CSM gave me dirty looks but deep down knew they couldn't say anything to me. During our TOA ceremony, I was one of two in my unit that WASN'T wearing the 44th MED BDE patch.

I haven't had this issue while with a unit, but I did have this issue with an ROTC cadet. Transitioning from an NCO just back from a deployment to a cadet wasn't easy for me at first. It's hard to let go of the NCO mentality. ROTC cadets wear a school patch in place of an OSSI patch while in uniform. I had an MS4 correct me on it the first week of my first semester. We got into a disagreement over it. I said I wouldn't switch them out, it was my option. Short story, the Cadre supported me, but I got lectured that cadets don't threaten to rip another cadet's arm off and beat them with it if they touch a combat patch.

Seems To be an Army issue. Marines don't have to worry about badges , patches other extraneous do dads. Name, rank, Marines is all that's needed. Back in my day no name. Unless things have changed of course. My signs AF attached to Army, he deployed wearing 10 Mountain patch, he's deployed now with 2/2 Stryker, for all intensive purposes he's now Army, except his SSGT rank.

The Army Times had a few articles on this in 2008. I was there when the 1ID CAB was trying to force TF Odin personnel (reservists) to wear the 1ID patch even if they were authorized to wear another patch. In the end, General Hertling had to put out a policy letter stating that Soldiers had the choice. The Commander and CSM then proceeded to act like asses and went to the chow hall, both wearing patches from their former units and marching down each aisle with their right sleeve in front going "see, see! We're cool, too!"
I had been wearing the 1ID patch but after that display....nope.

But also remember that during a ceremony, they can direct what you wear...TOA ceremonies and returning home are great examples.

Oh, and we display Esprit de Corps by us all wearing our patch on the left shoulder....

Personally I have never required any Soldier to wear a specific patch over another one, but have been in units that "highly suggested" we wear that unit patch if authorized. It is kind of like the 101st Airbirne Division "requiring" Soldiers to wear their Air Assault wings above the Airborne Wings, even though they both are the same class of badge. As others have said, I do believe it is for the esprit de corps and nothing else; show pride in the unit you are with.
I do wish people knew the regulations better though. I have copied and pasted an excerpt of AR 670-1 that pertains to this question about the SSI-FWTS.

(d) The Chief of Staff, Army must approve the authorization for wearing the SSI for FWTS.
(3) Unless otherwise approved by this regulation, Soldiers attached or under operational control (OPCON) to other services are not authorized to wear their patches as their SSI-FWTS without written approval from DCS, G-1 or a designated representative.
(4) Soldiers of all Army components (Active, ARNG, and USAR) who deploy during periods of service designated for wear of the SSI-FWTS are authorized to wear a SSI-FWTS. There are no time-in-theater requirements forauthorization to wear the SSI-FWTS. Soldiers may not earn more than one SSI-FWTS during the same deployment.(a) A deployed unit (company or higher) will wear its unit SSI as the SSI-FWTS, regardless of the headquarterselement deploying and the unit alignment or OPCON during the period of deployment.
(b) A deployed unit will not wear its assigned SSI as its SSI-FWTS when the SSI belongs to a major command, such as an ACOM/ASCC/DRU or State Area Command, or a non-deployable unit. In such cases, the unit will wear the SSI of the lowest echelon Army unit (company or higher) in the deployed chain of command as the SSI-FWTS. Whenthere is no intermediate unit (company or higher) in the deployed chain of command, these deployed Soldiers will wearthe SSI of the senior command in the theater as its SSI-FWTS.

I put that in here but can summarize in a few sentences. There was a comment about being able to choose from three different patches, that is incorrect, you are only authorized one per deployment. You cannot wear one from a different service and you must wear the patch of the unit you are assigned if your company or higher deploys.