It is generally wrong to describe P = IV as an inverse relationship between I and V. It would be right only if P were a constant.
In the 'usual' case of applying a p.d. V to a resistor of constant resistance R (i.e. the resistor obeys Ohm's law), if you double V, you will double I, and P (= IV) will go up by a factor of 4. So whatever you do to V, I will change proportionately, and P won't be constant, so P = IV doesn't give a relationship between I and V, it is simply a recipe for calculating P.
Your problem arises, I believe, because you've been required to consider how to get a given amount of power to a 'consumer'. And, using P = IV, you've thought 100 A and 10000 V would do just as well as 1000 A and 1000 V. This is true, but note that to take a current of 100 A at a p.d. of 10000 V, the consumer would have to have a resistance of 100 ohm, whereas to take a current of 1000 A at a p.d. of 1000V, the consumer would have to have a resistance of 1 ohm. So if we're considering ways of supplying the consumer with the same power at different voltages, the consumer must have different resistances in each case. That's why Ohm's law isn't applicable to the consumer in this type of calculation.
[Warning what follows is a bit compact and could cause (more?) confusion. If in doubt, I suggest you don't read it.] You might well ask: don't the end-users want a fixed voltage (110 V or 230 V or whatever)? Yes. What I've called 'the consumer' is in fact the input side of a transformer which steps the voltage down for the end users. A different transformer would have to be used if the transmission voltage going to the input of the transformer were changed. This changes the effective resistance of the consumer.