The explanation above is more a shortcut

You can think to the question both conceptually or picking numbers

1) xy<0 means that OR x OR y is negative and the other is positive. Both is not possible

when you have the first quantity, singularly, into the absolute value both must be positive regardless.

Instead in the second quantity it will become positive but AFTER inside you will perform the operation of subtraction. Therefore the number can be negative and then positive or positive and then positive.

In the first one is always positive

2) picking numbers

xy<0

x=-2 and y=3

|2|+|3|=|5|

|-2+3|=|1|

and the same is the other way around

A>B