Ohms law states "current is directly proportional to voltage". True, since more voltage will push more amps.

However, how am I getting this confused with the fact that everything in the real world suggests an inverse relationship between volts and current.

For example, a bigger load will decrease voltage. Or for high voltage transmission lines, the voltage is stepped up high so the lines can carry much less current and thus be very small.

where am I going wrong here?