How does investment in a bond mean positive duration and issuing a bond mean negative duration?

Because the formula starts with a negative:joy:

Seriously you are just buying in the risk while investing and shedding the same risk while issuing

Nothing more than a convention

Positive duration means that when interest rates fall, your net worth increases, and when they rise, your net worth decreases.

Negative duration means that when interest rates fall, your net worth decreases, and when they rise, your net worth increases.

When you are long a bond you are long duration ie you own this risk. This is the same as with equity - in both cases (duration and beta) we show the primary risk as being positive. As has already been mention, the formula for the duration effect takes into account this positive sign by inserting a negative sign.

Both long and short have risk; they’re equal in magnitude but opposite in sign.