When the sped difference is at its lowest or there is least resistance then the gear will be selected - correct?
For the point of argument, we'll say this is correct, although the gear is actually selected when the speeds are close enough for the teeth in the selector hub to slide over the dogteeth on the gear. This isn't the lowest speed difference, its simply less than the largest allowable speed difference. This can be felt by the 'snick' in a rushed gearchange (up or down) - thats actually the hub catching the weight of the gear because the snychros haven't matched the speeds exactly yet.
If at the point when the gearbox is in neutral and you are pushing against the syhncro and then you de-clutch again you are taking the spin off (or power from) the input shaft which means the gearbox is free-wheeling and you then let the clutch out again the input shaft starts to spin a different speed and the syhncro is sitting there spinning aagainst the cone (or gear being selected), thus causing extra wear. It is like having 2 bites at the cherry if you like.
This part, as Colin said, is incorrect. If you have pressure on the synchros when you are in neutral, then EVERY synchro in your gearbox is going to wear very fast. Why? Because most 5 speed boxes have 3 selector hubs (1st-2nd, 3rd-4th, and 5th). When your gearlever is in neutral, then the 1st/2nd hub is sitting exactly halfway between the gears it engages (hub centre is held in position by circlips either side), and likewise for 3rd/4th. 5th only usually has a gear on one side, so sits up against a washer on the opposite side to the gear. The hubs are held in this position by shift keys, which are small pieces of metal with a bump in them which sits into a groove running around the inside of the hub carrier. The keys have a spring running around on either side to exert force against these keys to lock them into the groove until they are moved by a positive force.
Now, when you select first (or second), the 1st/2nd hub has positive force exerted by the 1st/2nd selector fork, and it overcomes the 'detent' action of the shift keys, and at this point while you are pushing the gearlever to make the transition from no gear to a gear, the synchros are subject to friction - on one side by the cone which engages with the hub carrier, and on the other by the cone on the gear. It's worth noting that the cone on the hub side has dog teeth, and when you move the hub carrier across, it first engages the teeth on this previously freewheeling cone, and then holds it locked at mainshaft speed while continuing to slide over to engage on the dog teeth of the gear. Once the gear is selected, the synchro is effectively clamped between hub and gear, which are now splined together. But what happens to the 3rd/4th and the 5th gear hubs? Nothing, as the selector has not engaged with the 3rd/4th or 5th selector fork, so these hubs remain in the same position as they were while in neutral. Effectively, at all times a minimum of 3 gears in your gearbox are in exactly the same position as when in neutral.
They still spin, because they are constantly meshed with the cluster shaft (which in turn is constantly meshed with the input shaft), but they simply freewheel on the mainshaft. The shift hub assemblies are the only thing which cannot rotate on the mainshaft, as there are splines on the mainshaft, and splines on the inner (to enage permantly on the mainshaft) and outer (to prevent rotation of the hub carrier, which is the piece which actually engages the gear). When a gear is selected, the outer carrier moves to lock the gear to the mainshaft, but all the other gears still spin.
To get back to the original point, the only way for there to be force against the synchro when in neutral (failing a broken part in the hub allowing endfloat), is if you are actually pushing the gearlever at the time. Now I'm fairly sure most people aren't trying to push their gearlever into gear with the clutch up, so that would write that point off. The other thing you mentioned was when you let the clutch out again, the input shaft starts to spin at a different speed.... this is the whole point, is it not?
Lets take a hypothetical example:
Tailshaft is spinning at 3,000 rpm, thus the gearbox output shaft is spinning at same speed.
We will say this is in gear X, which has a 1:1 ratio, therefore the engine is now spinning at 3000rpm, as is the input shaft.
We now wish to change to gear Y, which has a 2:1 ratio. Assuming that the vehicle speed is the same, the output shaft continues to rotate at 3,000rpm, but the engine now needs to rotate at 6,000rpm. We could just bang it in, and let the synchros do the work of dragging the input shaft (simplified, see below) speed up by 3,000rpm, sure, and then let the clutch out and the gearbox can do the work of dragging the engine up those 3,000 rpm.
Which obviously is going to then create load all the way from the wheels through the driveline and into the engine.
But, if we burn a little extra fuel, and rev the engine up to 6,000rpm ourselves in neutral, while the output shaft is still turning at its 3,000rpm, how much work is the synchro doing then when we put the clutch back in and select the next gear? It doesn't have to drag an lazy input shaft up 3,000rpm (a shaft which instead of losing momentum due to lost engine drive, is actually likely to still be gaining momentum at the time its being acted on), all it needs to do a very minor position adjustment to allow the teeth to line up correctly, with no speed corrections.
You have to remember that most of the gearbox, except for the mainshaft itself, is actually always rotating when the input shaft is. Even when stationary in neutral, every single gear in that gearbox is turning. The mainshaft isn't, and neither are the shift hubs obviously, being splined on. Aside from 4th gear, the power goes in through the input shaft, then down into the cluster shaft, then up into the gears freewheeling on the mainshaft. When one of those mainshaft gears is locked to the mainshaft, and only then, you get drive coming out the back of the gearbox. The obvious effect of this, is although I said above the synchros are speeding up the input shaft, actually the synchro is altering the speed of everything between the mainshaft and the clutch - so all the gears inside the box, including the cluster shaft. If you've ever picked up a gearbox, about 30% of that weight is probably how much the synchro has to control.
Anyway, I'm sure someone will want to argue, or ask questions or whatever, and I've probably already gotten way too technical. If someone wants more tech or some clarification, feel free to ask, and I'll try to help, although I may require diagrams to do much better. If someone wants to argue, also fine, but be clear about what you're saying, and think it through first.