The reason you need to isolate the neutral in a sub panel is that the neutral is the only ground in the service panel.
There is nowhere else in your house where the white neutral conductor and the green bare ground conductor are connected.
In a normal situation the grounding conductor does not carry any type of current. As a result, there is no voltage drop.
If you would bond the ground and the neutral by the sub panel, any stray current can enter the equipment ground on any of the electrical items that are fed from this sub panel.
By isolating the ground and the neutral at the sub panel, the current goes to the main panel and finds its way to the service ground. You want to the equipment ground and the neutral at the main panel.
If this sounds remotely confusing, you need to contact a professional, licensed, insured electrician or electrical contractor to do the work. If this is done the wrong way, you have a chance of damaging the main panel as well as your electrical items. It is also possible to cause a fire.