Instructors need to teach methods that work for all, but when pressed you can get their preferred method.
While instructors tend to teach the method they believe will work best with all guns, they're sometimes just teaching their personal preferences -- and their reasons are often rationalizations (i.e., justification that may or may not be based in fact.)
Years ago, the argument against using anything but the "sling shot" release (in which the rear of the slide is grabbed like the pouch of a slingshot, and then pulled back and released) was chosen because it didn't require "FINE MOTOR SKILLS." That has been shown to be incorrect, and while it may work better for many folks, it's not because it only required "GROSS MOTOR SKILLS." It may work better because they don't give other methods much of a try! One gun mag, some years ago, did a live fire exercise, administered and supervised by an MD, in which the shooters were given injections of adrenaline/or similar (legal) stimulant and had them perform various drills.
The stimulant was used to simulate the normal shooter state when under duress, stress, or scared! It suggests that once you're stimulated, excited, alerted and your body starts into it's natural FIGHT/FLIGHT state, fine motor skills are something the instructor talks about, but in the real world they aren't all that noticeable. (Experience might make things better, as an experienced person might not roll into the FIGHT/FLIGHT state so easily.) In that exercise, people using either method had big problems. (Hand-over wasn't really talked about at the time, so we don't know how it might have fared.)
Unless they've changed again recently, the U.S. Army changed how it taught use of the M9 (and some other handguns) some years ago -- and taught the folks being trained to use the slide stop. (Note: if you can't access the slide release with the strong hand, you can use the off-hand thumb (or several fingers of the off-hand like a small claw) to hit the release. Using two or three fingers to gives you a bigger "slide-release tool" and you're less likely to miss the release or not press it completely.)
An acquaintance/instructor who worked with Special Ops troops (Special Forces, Delta, Marine Force Recon, etc.) at Ft. Bragg told me that this change was made after troops continued to have problems under combat conditions in Iraq and Afghanistan: they weren't making CLEAN releases, which meant that some of them would have to do a clearance drill or simply waste time getting the weapon running again. It was a problem probably caused by the fact that most wore gloves (due to cold temperatures in some areas, or rocky ground). Using the slide release (but not necessarily pressing it with the strong hand thumb) improved things a lot.
Using the Hand-Over release is preferred by many to the sling shot. This works well with most guns, but when used with the M9 it may decock the weapon or turn on the safety as the slide is grabbed and released --and that happens at the worst possible time!
Using the off-hand thumb or several fingers to release the slide can be quite efficient and rapid, according to that same acquaintance/instructor mentioned above. You just bring the off hand on up after you insert the magazine. That approach will also allows you to keep the weapon at or near eye level and pointed at the target (or ready to move to another target.) For most guns,
the Hand-Over method allows that too.
Both Handover and slide release methods, practiced and mastered, from last shot on target to the next shot on target,
can be noticeably faster than the slingshot approach.
The slingshot method is generally taught as part of the standard clearance drill -- and you want to know HOW to do it -- and the TAP, RACK, BANG drill (or TRB), even if you don't practice it as much as other drills/skills. (You can easily use the Hand-Over method in the TRB routine, too.)
In the final analysis, you should use the method that works best for you and your choice of weapons.
