Both reasons are perfectly valid and can happily be used as a tool within your training regime. The problem comes when these reasons become gospel. They are the rules and there is no deviating from them.
There is no doubt that progression is important for development when training and that utilizing reps as a method of tracking your progression is a useful tool. Having that target in mind is certainly a way of ensuring you push far enough to promote progression.
Keep in mind though, that, development is never linear. You can’t force a one or two rep progression with every workout. You may be able to for a few weeks, but eventually that progression will stop. That doesn’t mean, as is often claimed, that you have hit a plateau. More likely you have just spent the first few weeks becoming anatomically adapted to the movement, which made it look more like muscular progression. But it is often at this point that the real development starts.
In other words, constantly changing your routine whenever you appear to plateau is not as good an idea as it may appear.
Also, just because you can’t do more or even as much as you did previously, doesn’t necessarily mean you have gotten weaker. You could be just as strong, or perhaps stronger, but if you’ve had a long, stressful day or a poor night’s sleep, you can’t expect your body to perform optimally.
Not only that, but what if you are particularly invigorated on a particular day? Setting yourself a target could be very limiting.
Say you managed 10 reps last time, so today you are going to push out 12. What if you had enough in the tank for 15 or 16? You push to 12 and stop. After all you made your target. You have just lost the opportunity for an additional 3 or 4 reps.
So, you can see, using reps as a target is generally not the optimal way to train.
Not all reps are equal.
How you lift is crucial to the return you get. You should be looking to give your all in every rep. Either you should be lifting explosively with full contraction and constant tension on the muscle or carrying out controlled negatives enforcing your mind muscle connection etc.
Regardless of the technique you are employing, every rep requires you to give it your full, undivided attention.
If you are busy counting reps, that is just another distraction you don’t need and most likely you will start to think about how many you have left rather than making the most of the rep you are on.
It is for that reason that I generally prefer to work in the lower rep ranges.
Which brings us to reason number 2 – Different rep ranges should be used for different results.
It is issues like this that show the difference between pure science and real world application.
In a like for like situation it may well be mildly optimal for each result to be in the rep range described earlier. But regardless of your target, all rep ranges will show improvement. Low reps will cause hypertrophy and high reps will increase strength (assuming you are nutritionally set). However, working in the low rep range will allow you to maintain focus on each and every rep.
Generally, I have found that, above 6 reps, most people lose their intensity and focus and start looking to get through to the end.
You should always aim to do as much work as you can.
Your muscle fibres will always fire in order (smallest to largest) and the way to get to the larger fibres is to apply as much force from the muscle as possible.
The most common route for doing that is to add weight. But if you remember your high school physics, weight (or mass) is only part of the equation.
Force = Mass x Acceleration
So, the other factor is acceleration. If you accelerate a lighter weight faster than you would a heavy weight, you are potentially generating the same amount of force. To that end, the optimal movement would obviously be to accelerate a heavy weight fast.
If your target is hypertrophy, the convention might be to do 3 sets of 10.
But what if you did 10 sets of 3?
What if you just kept the rest periods short and gave your full focus to every one of the 3 reps?
You would be able to use a heavier weight, but you’d still do the same number of reps. The volume would be greater and you would have lifted with greater intensity. And if you are lifting at that low rep range, you don’t need to count. 3 is easy to track. And if you only do 2 or you do 4, so what?