One of the things that helped me really start to understand manual transmissions was to understand that there are actually 3 spinning things - the engine, the transmission, and the wheels. I mean sure, that's a simplification, in reality there are many more. But those are the big ones that you're controlling.
You have gauges for two of those things - the engine (tach) and the wheels (speedo). You do not get a gauge for the transmission, and it can be spinning very differently from the other two. Sliding the gear lever into gear creates a connection and synchronization between the transmission and the wheels. Releasing the clutch creates a connection between the engine and the transmission. When this is understood, seemingly innocuous driving habits, which your passenger and you might be unaware are causing problems, suddenly can be realized as creating significant stress. The example I gave in the opening was where the following happens:
Scenario 1
You're driving at 60 in 4th gear and approach a stoplight. You push the clutch, change into 1st gear at 60 mph, and brake to a stop.
Now, that might not even be possible to do, but let's analyze why it's bad. You're not going to destroy your engine, you've severed the connection between your engine and transmission. But what you're doing is connecting the wheels to the transmission at a gear ratio that is slightly insane for 60mph. So your transmission has to spin up to sync 1st gear to 60 mph. Which for 1st gear is probably well over 10,000 rpm.
I know that sounds crazy to some of you, but I've seen people do essentially that. Your passenger won't notice, and if your car lets you do it, you might not even be aware of it.
Scenario 2
Let's take a different example. You're driving at 60 in 4th gear and approach a stoplight. You push the clutch and change into neutral. With the clutch still in, at complete stop, you switch into 1st gear. The only thing we changed was shifting into neutral instead of first.
This seems much better. The car is stopped after all. The wheels are at zero rpm, the engine is near zero rpm. So what could be the problem with shifting into first? Well, the transmission is not at zero rpm or anywhere near, it's still spinning from when you disconnected it from the wheels (4th gear, 60mph). Now you have no way of knowing this of course. Because you have no gauge to tell you that it's spinning. You have to infer it from your actions. You shifted to neutral (severing transmission from the wheels) while it was spinning. And you never let the clutch out (synchronizing the transmission with the engine) while you were in neutral. So there is nothing but some internal friction (which is intentionally low) to slow the transmission down. So it's still spinning, whether you know it or not. You might think you're putting zero stress on it to slot it into first, but actually you're demanding that 1st gear synchros adjust the transmission spin down to zero.
Scenario 3
Let's take a different example. You're driving at 60 in 4th gear and approach a stoplight. You push the clutch but leave the car in 4th. With the clutch still in, at complete stop, you switch into 1st gear. The only thing we changed was leaving the lever in place until stop.
Now you've forced the transmission down to zero rpm because you left it connected to the wheels. So when you switch to first there is no synchro drag. From the outside, this looks entirely equivalent to the previous scenario. Internally, it's a ton less work for first gear synchronization.
Scenario 4
Let's take a different example. You're driving at 60 in 4th gear and approaching a stoplight. You push the clutch and change into neutral. You let the clutch out. At complete stop, you push the clutch back in and switch into 1st gear. The only thing changed between scenario 2 and this one is that you let the clutch out in neutral.
In this case, you've forced the transmission down to idle because you let the clutch out in neutral. You've used your clutch and engine to de-spin your transmission. Then when you're slotting it into first gear you're asking the synchros to adjust the speed of the transmission from idle to zero.
From the outside, these scenarios look the same. From the perspective of a passenger, and even a driver, they seem and feel the same. But in scenario 1, you're hammering 1st gear synchros. In scenario 2 you're asking them to do real work. In scenario 3, you're asking them to do no work, and in scenario 4 you're asking very minimal work of your clutch and synchros.
In short. This is why many people are terrible at driving manual transmissions. They don't understand them, and they just do what works, make a habit of it, and jog on. The repair bills come later, maybe even after they've dumped the car. Manual transmissions are just not for everyone. I know quite a few people who have driven or do currently drive stick who would not follow this explanation (I've tried to explain it to a few and lost them). They'll not see the difference between these scenarios. Because to lots of people, it's not about wheel speeds or engine speeds or synchronizing any of it, it's just memorization. Which gear should I be in now? I push this lever, move this thing, release lever, car goes. Asking them to think about what they're doing and why is like asking them to suddenly start writing with the other hand.